dotty: colored acceptance sets
This implement several new options for --dot in order to allow emptiness sets to be output as colored ⓿ or ❶... Also add a SPOT_DOTDEFAULT environment variable. * NEWS, src/bin/man/spot-x.x, src/bin/common_aoutput.cc, src/bin/dstar2tgba.cc: Document the new options. * doc/org/.dir-locals.el, doc/org/init.el.in: Setup SPOT_DOTEXTRA and SPOT_DOTDEFAULT for all documents. * doc/org/autfilt.org, doc/org/dstar2tgba.org, doc/org/ltl2tgba.org, doc/org/ltldo.org, doc/org/oaut.org, doc/org/randaut.org, doc/org/satmin.org: Adjust to this new setup. * src/misc/escape.cc, src/misc/escape.hh (escape_html): New function. * src/tgba/acc.cc, src/tgba/acc.hh (to_text, to_html): New method. * src/tgbaalgos/dotty.cc: Implement the new options. * src/tgbatest/readsave.test, wrap/python/tests/automata.ipynb: More tests. * wrap/python/spot.py: Make sure the default argument for dotty_reachable is None, so that SPOT_DOTDEFAULT is honored.
This commit is contained in:
Alexandre Duret-Lutz
parent
7caf2b83d6
commit
838bfb2ae3
21 changed files with 1500 additions and 1193 deletions
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@ -8,6 +8,8 @@
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(setq org-babel-sh-command (concat "PATH=../../src/bin"
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path-separator
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"$PATH sh"))
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(setenv "SPOT_DOTDEFAULT" "brf(Lato)")
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(setenv "SPOT_DOTEXTRA" "node[style=filled, fillcolor=\"#ffffa0\"]")
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(org-babel-do-load-languages 'org-babel-load-languages
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'((sh . t)
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(python . t)
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@ -27,7 +27,7 @@ same stream, =autfilt= will process them in batch.
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The output format can be controlled using [[file:oaut.org][the common output options]]
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(like =--spin=, =--lbtt=, =--dot=, =--hoaf=...).
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#+BEGIN_SRC sh :results verbatim :exports both
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#+BEGIN_SRC sh :results verbatim :exports code
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cat >example.hoa <<EOF
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HOA: v1
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States: 1
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@ -43,13 +43,18 @@ EOF
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autfilt example.hoa --dot
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#+END_SRC
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#+BEGIN_SRC sh :results verbatim :exports results
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SPOT_DOTEXTRA= autfilt example.hoa --dot=
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#+END_SRC
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#+RESULTS:
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: digraph G {
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: 0 [label="", style=invis, height=0]
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: 0 -> 1
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: 1 [label="0"]
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: 1 -> 1 [label="p0\n{0}"]
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: 1 -> 1 [label="!p0"]
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: rankdir=LR
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: I [label="", style=invis, width=0]
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: I -> 0
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: 0 [label="0"]
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: 0 -> 0 [label="p0\n{0}"]
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: 0 -> 0 [label="!p0"]
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: }
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The =--spin= options implicitly requires a degeneralization:
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@ -68,48 +68,58 @@ a Monitor, using the same options as [[file:ltl2tgba.org][=ltl2tgba=]].
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For instance here is the conversion to a Büchi automaton (=-B=) in [[http://http://www.graphviz.org/][GraphViz]]'s format:
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#+BEGIN_SRC sh :results verbatim :exports both
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#+BEGIN_SRC sh :results verbatim :exports code
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dstar2tgba -B fagfb
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#+END_SRC
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#+BEGIN_SRC sh :results verbatim :exports results
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SPOT_DOTEXTRA= dstar2tgba -B fagfb --dot=
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#+END_SRC
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#+RESULTS:
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#+begin_example
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digraph G {
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rankdir=LR
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I [label="", style=invis, width=0]
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I -> 0
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0 [label="0"]
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0 -> 0 [label="!a"]
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0 -> 1 [label="a"]
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1 [label="1", peripheries=2]
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1 -> 1 [label="b"]
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1 -> 2 [label="!b"]
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I -> 1
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0 [label="0", peripheries=2]
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0 -> 0 [label="b"]
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0 -> 2 [label="!b"]
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1 [label="1"]
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1 -> 0 [label="a"]
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1 -> 1 [label="!a"]
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2 [label="2"]
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2 -> 1 [label="b"]
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2 -> 0 [label="b"]
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2 -> 2 [label="!b"]
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}
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#+end_example
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Which can be rendered as:
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Which can be rendered as (note that in this documentation
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we use some [[file:aout.org][environement variables]] to produce a more colorful
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output by default):
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#+NAME: fagfb2ba
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#+BEGIN_SRC sh :results verbatim :exports none
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dstar2tgba -B fagfb | sed 's/\\/\\\\/'
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#+BEGIN_SRC sh :results verbatim :exports code
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dstar2tgba -B fagfb
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#+END_SRC
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#+RESULTS: fagfb2ba
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#+begin_example
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digraph G {
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rankdir=LR
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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node[style=filled, fillcolor="#ffffa0"]
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I [label="", style=invis, width=0]
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I -> 0
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0 [label="0"]
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0 -> 0 [label="!a"]
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0 -> 1 [label="a"]
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1 [label="1", peripheries=2]
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1 -> 1 [label="b"]
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1 -> 2 [label="!b"]
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I -> 1
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0 [label="0", peripheries=2]
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0 -> 0 [label=<b>]
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0 -> 2 [label=<!b>]
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1 [label="1"]
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1 -> 0 [label=<a>]
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1 -> 1 [label=<!a>]
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2 [label="2"]
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2 -> 1 [label="b"]
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2 -> 2 [label="!b"]
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2 -> 0 [label=<b>]
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2 -> 2 [label=<!b>]
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}
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#+end_example
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@ -153,7 +163,7 @@ T0_S3:
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Here is the translation of =GFa & GFb= to a 4-state Streett automaton:
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#+BEGIN_SRC sh :results verbatim :exports both
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ltlfilt -f 'GFa & GFb' -l | ltl2dstar --automata=streett --ltl2nba=spin:../../src/bin/ltl2tgba@-sD - gfagfb
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ltlfilt -f 'GFa & GFb' -l | ltl2dstar --automata=streett --ltl2nba=spin:ltl2tgba@-Ds - gfagfb
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cat gfagfb
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#+END_SRC
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#+RESULTS:
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@ -195,42 +205,27 @@ And now its conversion by =dstar2tgba= to a 2-state Büchi automaton.
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We don't pass any option to =dstar2tgba= because converting to TGBA in
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GraphViz's format is the default:
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#+NAME: gfagfb2ba
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#+BEGIN_SRC sh :results verbatim :exports code
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dstar2tgba gfagfb
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#+END_SRC
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#+RESULTS:
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#+begin_example
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digraph G {
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rankdir=LR
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I [label="", style=invis, width=0]
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I -> 0
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0 [label="0"]
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0 -> 1 [label="1"]
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1 [label="1"]
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1 -> 1 [label="!a & !b"]
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1 -> 1 [label="a & !b\n{0}"]
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1 -> 1 [label="!a & b\n{1}"]
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1 -> 1 [label="a & b\n{0,1}"]
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}
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#+end_example
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#+NAME: gfagfb2ba
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#+BEGIN_SRC sh :results verbatim :exports none
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dstar2tgba gfagfb | sed 's/\\/\\\\/g'
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#+END_SRC
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#+RESULTS: gfagfb2ba
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#+begin_example
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digraph G {
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rankdir=LR
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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node[style=filled, fillcolor="#ffffa0"]
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I [label="", style=invis, width=0]
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I -> 0
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0 [label="0"]
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0 -> 1 [label="1"]
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0 -> 1 [label=<1>]
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1 [label="1"]
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1 -> 1 [label="!a & !b"]
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1 -> 1 [label="a & !b\\n{0}"]
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1 -> 1 [label="!a & b\\n{1}"]
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1 -> 1 [label="a & b\\n{0,1}"]
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1 -> 1 [label=<!a & !b>]
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1 -> 1 [label=<a & !b<br/><font color="#5DA5DA">⓿</font>>]
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1 -> 1 [label=<!a & b<br/><font color="#F17CB0">❶</font>>]
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1 -> 1 [label=<a & b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
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}
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#+end_example
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@ -355,33 +350,33 @@ head -n 10 |
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while read f; do
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echo "$f"
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ltlfilt -l -f "$f" |
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ltl2dstar --ltl2nba=spin:../../src/bin/ltl2tgba@-sD - - |
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ltl2dstar --ltl2nba=spin:../../src/bin/ltl2tgba@-Ds - - |
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dstar2tgba -B --stats=' DRA: %Sst.; BA: %sst.; det.? %d; complete? %p'
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done
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#+END_SRC
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#+RESULTS:
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#+begin_example
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c U (c & (a | b | (Xc U (a & Xc))))
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DRA: 3st.; BA: 2st.; det.? 1; complete? 0
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!b | F!c
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DRA: 3st.; BA: 3st.; det.? 1; complete? 1
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(!a R F!b) R !b
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DRA: 6st.; BA: 5st.; det.? 1; complete? 0
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b U !c
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DRA: 3st.; BA: 2st.; det.? 1; complete? 0
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(b | Fa) R Fc
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DRA: 9st.; BA: 6st.; det.? 1; complete? 1
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Ga U (Gc R (!a | Gc))
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DRA: 7st.; BA: 7st.; det.? 0; complete? 0
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GFc
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DRA: 3st.; BA: 3st.; det.? 1; complete? 1
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(F!c U a) R !a
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DRA: 6st.; BA: 5st.; det.? 1; complete? 0
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b | G!b
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DRA: 4st.; BA: 3st.; det.? 1; complete? 0
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!a R (!c & (!a | (F!b U (!a & F!b))))
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DRA: 5st.; BA: 4st.; det.? 1; complete? 0
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F(a & !b & G!c)
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DRA: 2st.; BA: 3st.; det.? 0; complete? 0
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GF!c
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DRA: 3st.; BA: 3st.; det.? 1; complete? 1
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!a | (a R b)
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DRA: 3st.; BA: 2st.; det.? 1; complete? 0
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Xc R (G!c R (b | G!c))
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DRA: 4st.; BA: 2st.; det.? 1; complete? 0
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c & G(b | F(a & c))
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DRA: 5st.; BA: 3st.; det.? 1; complete? 0
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XXFc
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DRA: 4st.; BA: 4st.; det.? 1; complete? 1
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XFc | Gb
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DRA: 5st.; BA: 4st.; det.? 1; complete? 1
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G(((!a & Gc) | (a & F!c)) U (!a | Ga))
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DRA: 6st.; BA: 5st.; det.? 1; complete? 1
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a & !b
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DRA: 3st.; BA: 2st.; det.? 1; complete? 0
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#+end_example
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An important point you should be aware of when comparing these numbers
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@ -426,6 +421,6 @@ states and $n$ acceptance pairs. Our translation to TGBA limits this
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to $|Q|\cdot(2^n+1)$ states.
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Sometimes, as in the [[#streett_to_tgba_example][example for =GFa & GFb=]] the output of this
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conversion will happen to be deterministic. Let's say that this is
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luck: Spot does not implement any algorithm to preserve the
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determinism of Streett automata.
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conversion happens to be deterministic. This is pure luck: Spot does
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not implement any algorithm to preserve the determinism of Streett
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automata.
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@ -24,6 +24,9 @@
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(setq org-babel-sh-command
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(concat "PATH=@abs_top_builddir@/src/bin" path-separator "$PATH sh"))
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(setenv "SPOT_DOTDEFAULT" "brf(Lato)")
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(setenv "SPOT_DOTEXTRA" "node[style=filled, fillcolor=\"#ffffa0\"]")
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(setq org-export-html-home/up-format
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"<div id=\"org-div-home-and-up\" style=\"text-align:center;white-space:nowrap;\">
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<a accesskey=\"h\" href=\"%s\">UP</a> | <a accesskey=\"H\" href=\"%s\">HOME</a>
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@ -14,9 +14,12 @@ option.
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Formulas to translate may be specified using [[file:ioltl.org][common input options for
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LTL/PSL formulas]].
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#+BEGIN_SRC sh :results verbatim :exports both
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -f 'Fa & GFb'
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#+END_SRC
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#+BEGIN_SRC sh :results verbatim :exports results
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SPOT_DOTEXTRA= ltl2tgba -f 'Fa & GFb' --dot=
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#+END_SRC
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#+RESULTS:
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#+begin_example
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digraph G {
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@ -47,23 +50,29 @@ ltl2tgba "Fa & GFb" | dot -Tpdf > tgba.pdf
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#+END_SRC
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#+RESULTS:
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The result would look like this:
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The result would look like this (note that in this documentation
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we use some [[file:aout.org][environement variables]] to produce a more colorful
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output by default)
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#+NAME: dotex
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#+BEGIN_SRC sh :results verbatim :exports none
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ltl2tgba "Fa & GFb" | sed 's/\\/\\\\/'
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ltl2tgba "Fa & GFb"
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#+END_SRC
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#+RESULTS: dotex
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#+begin_example
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digraph G {
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rankdir=LR
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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node[style=filled, fillcolor="#ffffa0"]
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I [label="", style=invis, width=0]
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I -> 1
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0 [label="0"]
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0 -> 0 [label="b\\n{0}"]
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0 -> 0 [label="!b"]
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0 -> 0 [label=<b<br/><font color="#5DA5DA">⓿</font>>]
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0 -> 0 [label=<!b>]
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1 [label="1"]
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1 -> 0 [label="a"]
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1 -> 1 [label="!a"]
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1 -> 0 [label=<a>]
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1 -> 1 [label=<!a>]
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}
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#+end_example
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@ -74,53 +83,39 @@ $txt
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#+RESULTS:
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[[file:dotex.png]]
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The string between braces, ={0}=, represents the sets of acceptance
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sets a transition belongs to. In this case, there is only one
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acceptance set, called =0=, containing a single transition. You may
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have many transitions in the same acceptance set, and a transition may
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also belong to multiple acceptance sets. An infinite path through
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this automaton is accepting iff it visit each acceptance set
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infinitely often. Therefore, in the above example, any accepted path
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will /necessarily/ leave the initial state after a finite amount of
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steps, and then it will verify the property =b= infinitely often. It
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is also possible that an automaton do not use any acceptance set at
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all, in which any run is accepting.
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Characters like ⓿, ❶, etc. denotes the acceptance sets a transition
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belongs to. In this case, there is only one acceptance set, called
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=0=, containing a single transition. You may have many transitions in
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the same acceptance set, and a transition may also belong to multiple
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acceptance sets. An infinite path through this automaton is accepting
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iff it visit each acceptance set infinitely often. Therefore, in the
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above example, any accepted path will /necessarily/ leave the initial
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state after a finite amount of steps, and then it will verify the
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property =b= infinitely often. It is also possible that an automaton
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do not use any acceptance set at all, in which any run is accepting.
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Here is a TGBA with multiple acceptance sets (we omit the call to
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=dot= to render the output of =ltl2tgba= from now on):
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba 'GFa & GFb'
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#+END_SRC
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#+RESULTS:
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#+begin_example
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digraph G {
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rankdir=LR
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I [label="", style=invis, width=0]
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I -> 0
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0 [label="0"]
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0 -> 0 [label="a & b\n{0,1}"]
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0 -> 0 [label="!a & !b"]
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0 -> 0 [label="!a & b\n{1}"]
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0 -> 0 [label="a & !b\n{0}"]
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}
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#+end_example
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#+NAME: dotex2
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#+BEGIN_SRC sh :results verbatim :exports none
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ltl2tgba "GFa & GFb" | sed 's/\\/\\\\/'
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba "GFa & GFb"
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#+END_SRC
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#+RESULTS: dotex2
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#+begin_example
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digraph G {
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rankdir=LR
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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node[style=filled, fillcolor="#ffffa0"]
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I [label="", style=invis, width=0]
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I -> 0
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0 [label="0"]
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0 -> 0 [label="a & b\\n{0,1}"]
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0 -> 0 [label="!a & !b"]
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0 -> 0 [label="!a & b\\n{1}"]
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0 -> 0 [label="a & !b\\n{0}"]
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0 -> 0 [label=<a & b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
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0 -> 0 [label=<!a & !b>]
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0 -> 0 [label=<!a & b<br/><font color="#F17CB0">❶</font>>]
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0 -> 0 [label=<a & !b<br/><font color="#5DA5DA">⓿</font>>]
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}
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#+end_example
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@ -130,57 +125,38 @@ $txt
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#+RESULTS:
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[[file:dotex2.png]]
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|
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The above TGBA has two acceptance sets: =0= and =1=. The position of
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The above TGBA has two acceptance sets: ⓿ and ❶. The position of
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these acceptance sets ensures that atomic propositions =a= and =b= must
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be true infinitely often.
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A Büchi automaton for the previous formula can be obtained with the
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||||
=-B= option:
|
||||
|
||||
#+NAME: dotex2ba
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -B 'GFa & GFb'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="a & b"]
|
||||
0 -> 1 [label="!b"]
|
||||
0 -> 2 [label="!a & b"]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="a & b"]
|
||||
1 -> 1 [label="!b"]
|
||||
1 -> 2 [label="!a & b"]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a"]
|
||||
2 -> 2 [label="!a"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: dotex2ba
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -B 'GFa & GFb' | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
#+RESULTS: dotex2ba
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="a & b"]
|
||||
0 -> 1 [label="!b"]
|
||||
0 -> 2 [label="!a & b"]
|
||||
0 -> 0 [label=<a & b>]
|
||||
0 -> 1 [label=<!b>]
|
||||
0 -> 2 [label=<!a & b>]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="a & b"]
|
||||
1 -> 1 [label="!b"]
|
||||
1 -> 2 [label="!a & b"]
|
||||
1 -> 0 [label=<a & b>]
|
||||
1 -> 1 [label=<!b>]
|
||||
1 -> 2 [label=<!a & b>]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a"]
|
||||
2 -> 2 [label="!a"]
|
||||
2 -> 0 [label=<a>]
|
||||
2 -> 2 [label=<!a>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -201,48 +177,33 @@ is done internally):
|
|||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba --dot=t -B 'GFa & GFb'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 0 [label="a & b\n{0}"]
|
||||
0 -> 1 [label="!b\n{0}"]
|
||||
0 -> 2 [label="!a & b\n{0}"]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="a & b"]
|
||||
1 -> 1 [label="!b"]
|
||||
1 -> 2 [label="!a & b"]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a"]
|
||||
2 -> 2 [label="!a"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: dotex2ba-t
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba --dot=t -B 'GFa & GFb' | sed 's/\\/\\\\/'
|
||||
ltl2tgba --dot=.t -B 'GFa & GFb'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: dotex2ba-t
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 0 [label="a & b\\n{0}"]
|
||||
0 -> 1 [label="!b\\n{0}"]
|
||||
0 -> 2 [label="!a & b\\n{0}"]
|
||||
0 -> 0 [label=<a & b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
0 -> 1 [label=<!b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
0 -> 2 [label=<!a & b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="a & b"]
|
||||
1 -> 1 [label="!b"]
|
||||
1 -> 2 [label="!a & b"]
|
||||
1 -> 0 [label=<a & b>]
|
||||
1 -> 1 [label=<!b>]
|
||||
1 -> 2 [label=<!a & b>]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a"]
|
||||
2 -> 2 [label="!a"]
|
||||
2 -> 0 [label=<a>]
|
||||
2 -> 2 [label=<!a>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -262,18 +223,28 @@ ltl2tgba --help | sed -n '/Output format:/,/^$/p' | sed '1d;$d'
|
|||
#+begin_example
|
||||
-8, --utf8 enable UTF-8 characters in output (ignored with
|
||||
--lbtt or --spin)
|
||||
--dot[=c|h|n|N|s|t|v] GraphViz's format (default). Add letters to chose
|
||||
(c) circular nodes, (h) horizontal layout, (v)
|
||||
vertical layout, (n) with name, (N) without name,
|
||||
(s) with SCCs, (t) always transition-based
|
||||
--dot[=a|b|c|f(FONT)|h|n|N|r|R|s|t|v]
|
||||
GraphViz's format (default). Add letters for (a)
|
||||
acceptance display, (b) acceptance sets as
|
||||
bullets,(c) circular nodes, (f(FONT)) use FONT,
|
||||
(h) horizontal layout, (v) vertical layout, (n)
|
||||
with name, (N) without name, (r) rainbow colors
|
||||
for acceptance set, (R) color acceptance set by
|
||||
Inf/Fin, (s) with SCCs, (t) force transition-based
|
||||
acceptance.
|
||||
-H, --hoaf[=s|t|m|l] Output the automaton in HOA format. Add letters
|
||||
to select (s) state-based acceptance, (t)
|
||||
transition-based acceptance, (m) mixed acceptance,
|
||||
(l) single-line output
|
||||
-H, --hoaf[=i|s|t|m|l] Output the automaton in HOA format. Add letters
|
||||
to select (i) use implicit labels for complete
|
||||
deterministic automata, (s) prefer state-based
|
||||
acceptance when possible [default], (t) force
|
||||
transition-based acceptance, (m) mix state and
|
||||
transition-based acceptance, (l) single-line
|
||||
output
|
||||
--lbtt[=t] LBTT's format (add =t to force transition-based
|
||||
acceptance even on Büchi automata)
|
||||
--name=FORMAT set the name of the output automaton
|
||||
-o, --output=FORMAT send output to a file named FORMAT instead of
|
||||
standard output. The first automaton sent to a
|
||||
file truncates it unless FORMAT starts with '>>'.
|
||||
-q, --quiet suppress all normal output
|
||||
-s, --spin[=6|c] Spin neverclaim (implies --ba). Add letters to
|
||||
select (6) Spin's 6.2.4 style, (c) comments on
|
||||
|
|
@ -284,50 +255,31 @@ ltl2tgba --help | sed -n '/Output format:/,/^$/p' | sed '1d;$d'
|
|||
Option =-8= can be used to improve the readability of the output
|
||||
if your system can display UTF-8 correctly.
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -B8 'GFa & GFb'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="a∧b"]
|
||||
0 -> 1 [label="b̅"]
|
||||
0 -> 2 [label="a̅∧b"]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="a∧b"]
|
||||
1 -> 1 [label="b̅"]
|
||||
1 -> 2 [label="a̅∧b"]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a"]
|
||||
2 -> 2 [label="a̅"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: dotex2ba8
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -B8 "GFa & GFb" | sed 's/\\/\\\\/'
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -B8 "GFa & GFb"
|
||||
#+END_SRC
|
||||
#+RESULTS: dotex2ba8
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="a∧b"]
|
||||
0 -> 1 [label="b̅"]
|
||||
0 -> 2 [label="a̅∧b"]
|
||||
0 -> 0 [label=<a∧b>]
|
||||
0 -> 1 [label=<b̅>]
|
||||
0 -> 2 [label=<a̅∧b>]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="a∧b"]
|
||||
1 -> 1 [label="b̅"]
|
||||
1 -> 2 [label="a̅∧b"]
|
||||
1 -> 0 [label=<a∧b>]
|
||||
1 -> 1 [label=<b̅>]
|
||||
1 -> 2 [label=<a̅∧b>]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a"]
|
||||
2 -> 2 [label="a̅"]
|
||||
2 -> 0 [label=<a>]
|
||||
2 -> 2 [label=<a̅>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -423,48 +375,30 @@ automaton.
|
|||
An example formula where the difference between =-D= and =--small= is
|
||||
flagrant is =Ga|Gb|Gc=:
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba 'Ga|Gb|Gc'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 1 [label="a"]
|
||||
0 -> 2 [label="b"]
|
||||
0 -> 3 [label="c"]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 1 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="b"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 3 [label="c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: gagbgc1
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba "Ga|Gb|Gc" | sed 's/\\/\\\\/'
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba "Ga|Gb|Gc"
|
||||
#+END_SRC
|
||||
#+RESULTS: gagbgc1
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 1 [label="a"]
|
||||
0 -> 2 [label="b"]
|
||||
0 -> 3 [label="c"]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 1 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="b"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 3 [label="c"]
|
||||
0 [label="0"]
|
||||
0 -> 1 [label=<a>]
|
||||
0 -> 2 [label=<b>]
|
||||
0 -> 3 [label=<c>]
|
||||
1 [label="1"]
|
||||
1 -> 1 [label=<a>]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label=<b>]
|
||||
3 [label="3"]
|
||||
3 -> 3 [label=<c>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -474,80 +408,46 @@ $txt
|
|||
#+RESULTS:
|
||||
[[file:gagbgc1.png]]
|
||||
|
||||
#+NAME: gagbgc2
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -D 'Ga|Gb|Gc'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 6
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="c"]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 0 [label="!b & c"]
|
||||
1 -> 1 [label="b & c"]
|
||||
1 -> 2 [label="b & !c"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="b"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 2 [label="!a & b"]
|
||||
3 -> 3 [label="a & b"]
|
||||
3 -> 5 [label="a & !b"]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 0 [label="!a & c"]
|
||||
4 -> 4 [label="a & c"]
|
||||
4 -> 5 [label="a & !c"]
|
||||
5 [label="5", peripheries=2]
|
||||
5 -> 5 [label="a"]
|
||||
6 [label="6", peripheries=2]
|
||||
6 -> 0 [label="!a & !b & c"]
|
||||
6 -> 1 [label="!a & b & c"]
|
||||
6 -> 2 [label="!a & b & !c"]
|
||||
6 -> 3 [label="a & b & !c"]
|
||||
6 -> 4 [label="a & !b & c"]
|
||||
6 -> 5 [label="a & !b & !c"]
|
||||
6 -> 6 [label="a & b & c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: gagbgc2
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -D 'Ga|Gb|Gc' | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
#+RESULTS: gagbgc2
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 6
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="c"]
|
||||
0 -> 0 [label=<c>]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 0 [label="!b & c"]
|
||||
1 -> 1 [label="b & c"]
|
||||
1 -> 2 [label="b & !c"]
|
||||
1 -> 0 [label=<!b & c>]
|
||||
1 -> 1 [label=<b & c>]
|
||||
1 -> 2 [label=<b & !c>]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="b"]
|
||||
2 -> 2 [label=<b>]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 2 [label="!a & b"]
|
||||
3 -> 3 [label="a & b"]
|
||||
3 -> 5 [label="a & !b"]
|
||||
3 -> 2 [label=<!a & b>]
|
||||
3 -> 3 [label=<a & b>]
|
||||
3 -> 5 [label=<a & !b>]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 0 [label="!a & c"]
|
||||
4 -> 4 [label="a & c"]
|
||||
4 -> 5 [label="a & !c"]
|
||||
4 -> 0 [label=<!a & c>]
|
||||
4 -> 4 [label=<a & c>]
|
||||
4 -> 5 [label=<a & !c>]
|
||||
5 [label="5", peripheries=2]
|
||||
5 -> 5 [label="a"]
|
||||
5 -> 5 [label=<a>]
|
||||
6 [label="6", peripheries=2]
|
||||
6 -> 0 [label="!a & !b & c"]
|
||||
6 -> 1 [label="!a & b & c"]
|
||||
6 -> 2 [label="!a & b & !c"]
|
||||
6 -> 3 [label="a & b & !c"]
|
||||
6 -> 4 [label="a & !b & c"]
|
||||
6 -> 5 [label="a & !b & !c"]
|
||||
6 -> 6 [label="a & b & c"]
|
||||
6 -> 0 [label=<!a & !b & c>]
|
||||
6 -> 1 [label=<!a & b & c>]
|
||||
6 -> 2 [label=<!a & b & !c>]
|
||||
6 -> 3 [label=<a & b & !c>]
|
||||
6 -> 4 [label=<a & !b & c>]
|
||||
6 -> 5 [label=<a & !b & !c>]
|
||||
6 -> 6 [label=<a & b & c>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -701,47 +601,30 @@ compatible outgoing transition exist.
|
|||
-MD= (short for =--monitor --deterministic=) will output the minimal
|
||||
deterministic monitor for the given formula.
|
||||
|
||||
#+NAME: monitor1
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -M '(Xa & Fb) | Gc'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 1 [label="1"]
|
||||
0 -> 3 [label="c"]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 2 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="1"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 3 [label="c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: monitor1
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -M '(Xa & Fb) | Gc' | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: monitor1
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 1 [label="1"]
|
||||
0 -> 3 [label="c"]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 2 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="1"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 3 [label="c"]
|
||||
0 [label="0"]
|
||||
0 -> 1 [label=<1>]
|
||||
0 -> 3 [label=<c>]
|
||||
1 [label="1"]
|
||||
1 -> 2 [label=<a>]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label=<1>]
|
||||
3 [label="3"]
|
||||
3 -> 3 [label=<c>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -752,53 +635,33 @@ $txt
|
|||
#+RESULTS:
|
||||
[[file:monitor1.png]]
|
||||
|
||||
#+NAME: monitor2
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -MD '(Xa & Fb) | Gc'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 3
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="1"]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 0 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="c"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 1 [label="!c"]
|
||||
3 -> 4 [label="c"]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 0 [label="a"]
|
||||
4 -> 2 [label="!a & c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: monitor2
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -MD '(Xa & Fb) | Gc' | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: monitor2
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 3
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="1"]
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 0 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="c"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 1 [label="!c"]
|
||||
3 -> 4 [label="c"]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 0 [label="a"]
|
||||
4 -> 2 [label="!a & c"]
|
||||
0 [label="0"]
|
||||
0 -> 0 [label=<1>]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label=<a>]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label=<c>]
|
||||
3 [label="3"]
|
||||
3 -> 1 [label=<!c>]
|
||||
3 -> 4 [label=<c>]
|
||||
4 [label="4"]
|
||||
4 -> 0 [label=<a>]
|
||||
4 -> 2 [label=<!a & c>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -811,7 +674,8 @@ $txt
|
|||
|
||||
Because they accept all finite executions that could be extended to
|
||||
match the formula, monitor cannot be used to check for eventualities
|
||||
such as =F(a)=. Any finite execution can be extended to match =F(a)=.
|
||||
such as =F(a)=: indeed, any finite execution can be extended to match
|
||||
=F(a)=.
|
||||
|
||||
# LocalWords: ltl tgba num toc PSL Büchi automata SRC GFb invis Acc
|
||||
# LocalWords: ltlfilt filenames GraphViz vectorial pdf Tpdf dotex
|
||||
|
|
|
|||
|
|
@ -312,13 +312,16 @@ the following words, then the string on the right is appended.
|
|||
|
||||
So for instance you can type just
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports both
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltldo ltl2ba -f a
|
||||
#+END_SRC
|
||||
|
||||
to obtain a Dot output (this is the default output format for =ltldo=)
|
||||
for the neverclaim produced by =ltl2ba -f a=.
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports result
|
||||
SPOT_DOTEXTRA= ltldo ltl2ba -f a --dot=
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
: digraph G {
|
||||
: rankdir=LR
|
||||
|
|
|
|||
325
doc/org/oaut.org
325
doc/org/oaut.org
|
|
@ -1,4 +1,4 @@
|
|||
# -*- coding: utf-8 -*-
|
||||
y# -*- coding: utf-8 -*-
|
||||
#+TITLE: Common output options for automata
|
||||
#+SETUPFILE: setup.org
|
||||
#+HTML_LINK_UP: tools.html
|
||||
|
|
@ -18,16 +18,22 @@ ltl2tgba --help | sed -n '/Output format:/,/^$/p' | sed '1d;$d'
|
|||
#+begin_example
|
||||
-8, --utf8 enable UTF-8 characters in output (ignored with
|
||||
--lbtt or --spin)
|
||||
--dot[=c|h|n|N|s|t|v] GraphViz's format (default). Add letters for (a)
|
||||
acceptance display, (c) circular nodes, (h)
|
||||
horizontal layout, (v) vertical layout, (n) with
|
||||
name, (N) without name, (s) with SCCs, (t) force
|
||||
transition-based acceptance.
|
||||
-H, --hoaf[=s|t|m|l] Output the automaton in HOA format. Add letters
|
||||
to select (s) prefer state-based acceptance when
|
||||
possible [default], (t) force transition-based
|
||||
acceptance, (m) mix state and transition-based
|
||||
acceptance, (l) single-line output
|
||||
--dot[=a|b|c|f(FONT)|h|n|N|r|R|s|t|v]
|
||||
GraphViz's format (default). Add letters for (a)
|
||||
acceptance display, (b) acceptance sets as
|
||||
bullets,(c) circular nodes, (f(FONT)) use FONT,
|
||||
(h) horizontal layout, (v) vertical layout, (n)
|
||||
with name, (N) without name, (r) rainbow colors
|
||||
for acceptance set, (R) color acceptance set by
|
||||
Inf/Fin, (s) with SCCs, (t) force transition-based
|
||||
acceptance.
|
||||
-H, --hoaf[=i|s|t|m|l] Output the automaton in HOA format. Add letters
|
||||
to select (i) use implicit labels for complete
|
||||
deterministic automata, (s) prefer state-based
|
||||
acceptance when possible [default], (t) force
|
||||
transition-based acceptance, (m) mix state and
|
||||
transition-based acceptance, (l) single-line
|
||||
output
|
||||
--lbtt[=t] LBTT's format (add =t to force transition-based
|
||||
acceptance even on Büchi automata)
|
||||
--name=FORMAT set the name of the output automaton
|
||||
|
|
@ -118,148 +124,161 @@ represent. Here is a picture of these two automata:
|
|||
|
||||
#+NAME: hoafex
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba --dot=cn '(Ga -> Gb) W c' 'a U b' | dot | gvpack |
|
||||
ltl2tgba --dot=.cn '(Ga -> Gb) W c' 'a U b' | dot | gvpack |
|
||||
perl -pe 's/\\\n//g;s/\\/\\\\/g;s/graph G/graph cluster/g'
|
||||
#+END_SRC
|
||||
#+RESULTS: hoafex
|
||||
#+begin_example
|
||||
digraph root {
|
||||
graph [bb="0,0,425,231.06",
|
||||
graph [bb="0,0,427,231.07",
|
||||
fontname=Lato,
|
||||
labelloc=t,
|
||||
lheight=0.21,
|
||||
rankdir=LR
|
||||
];
|
||||
node [label="\\N",
|
||||
shape=circle
|
||||
node [fillcolor="#ffffa0",
|
||||
fontname=Lato,
|
||||
label="\\N",
|
||||
shape=circle,
|
||||
style=filled
|
||||
];
|
||||
edge [fontname=Lato];
|
||||
subgraph cluster {
|
||||
graph [bb="",
|
||||
label="(Gb | F!a) W c",
|
||||
fontname=Lato,
|
||||
label=<(Gb | F!a) W c>,
|
||||
labelloc=t,
|
||||
lheight=0.21,
|
||||
lp="196.5,196.66",
|
||||
lwidth=1.14,
|
||||
lp="197.5,196.66",
|
||||
lwidth=1.19,
|
||||
rankdir=LR
|
||||
];
|
||||
node [height="",
|
||||
node [fillcolor="#ffffa0",
|
||||
fontname=Lato,
|
||||
height="",
|
||||
label="\\N",
|
||||
pos="",
|
||||
shape=circle,
|
||||
style="",
|
||||
style=filled,
|
||||
width=""
|
||||
];
|
||||
edge [label="",
|
||||
edge [fontname=Lato,
|
||||
label="",
|
||||
lp="",
|
||||
pos=""
|
||||
];
|
||||
I [height=0.013889,
|
||||
label="",
|
||||
pos="1,49.162",
|
||||
pos="1,49.168",
|
||||
style=invis,
|
||||
width=0.013889];
|
||||
1 [height=0.5,
|
||||
label=1,
|
||||
pos="56,49.162",
|
||||
pos="56,49.168",
|
||||
width=0.5];
|
||||
I -> 1 [pos="e,37.942,49.324 1.1549,49.324 2.6725,49.324 15.097,49.324 27.628,49.324"];
|
||||
1 -> 1 [label="!a & !c\\n{0}",
|
||||
1 -> 1 [label=<!a & !c<br/><font color="#5DA5DA">⓿</font>>,
|
||||
lp="56,100.32",
|
||||
pos="e,62.379,66.361 49.621,66.361 48.319,76.181 50.445,85.324 56,85.324 59.472,85.324 61.604,81.752 62.398,76.677"];
|
||||
pos="e,62.379,66.362 49.621,66.362 48.319,76.182 50.445,85.324 56,85.324 59.472,85.324 61.604,81.753 62.398,76.677"];
|
||||
0 [height=0.5,
|
||||
label=0,
|
||||
pos="189,121.16",
|
||||
pos="190,121.17",
|
||||
width=0.5];
|
||||
1 -> 0 [label="a & b & !c",
|
||||
lp="122.5,113.82",
|
||||
pos="e,171.82,115.02 70.135,60.558 76.501,65.71 84.4,71.688 92,76.324 114.85,90.263 142.72,102.89 162.53,111.19"];
|
||||
1 -> 0 [label=<a & b & !c>,
|
||||
lp="123,113.83",
|
||||
pos="e,172.99,115.19 70.127,60.572 76.491,65.727 84.391,71.704 92,76.324 115.21,90.42 143.57,103.1 163.61,111.38"];
|
||||
2 [height=0.5,
|
||||
label=2,
|
||||
pos="189,34.162",
|
||||
pos="190,34.168",
|
||||
width=0.5];
|
||||
1 -> 2 [label="a & !c",
|
||||
lp="122.5,64.823",
|
||||
pos="e,174.09,44.491 73.626,53.241 93.026,57.118 125.9,61.52 153,54.324 157.19,53.213 161.39,51.47 165.37,49.466"];
|
||||
1 -> 2 [label=<a & !c>,
|
||||
lp="123,64.824",
|
||||
pos="e,175.09,44.492 73.8,53.268 93.402,57.17 126.62,61.596 154,54.324 158.19,53.213 162.39,51.47 166.37,49.467"];
|
||||
3 [height=0.5,
|
||||
label=3,
|
||||
pos="375,34.162",
|
||||
pos="377,34.168",
|
||||
width=0.5];
|
||||
1 -> 3 [label=c,
|
||||
lp="240.5,9.8235",
|
||||
pos="e,359.03,25.984 66.028,34.328 72.163,25.634 81.128,15.425 92,10.324 114,0 275.42,0.3271 310,7.3235 323.76,10.107 338.24,15.942 349.94,21.478"];
|
||||
0 -> 0 [label="b\\n{0}",
|
||||
lp="189,172.32",
|
||||
pos="e,197.63,137.24 180.37,137.24 178.11,147.47 180.99,157.32 189,157.32 194.26,157.32 197.3,153.08 198.14,147.27"];
|
||||
2 -> 1 [label="!a & !c\\n{0}",
|
||||
lp="122.5,35.324",
|
||||
pos="e,68.596,36.184 172.36,26.591 166.44,24.064 159.55,21.586 153,20.324 126.38,15.197 117.5,11.13 92,20.324 86.432,22.331 81.123,25.651 76.398,29.343"];
|
||||
2 -> 2 [label="a & !c",
|
||||
lp="189,77.824",
|
||||
pos="e,197.63,50.24 180.37,50.24 178.11,60.474 180.99,70.324 189,70.324 194.26,70.324 197.3,66.082 198.14,60.273"];
|
||||
2 -> 3 [label="!a & c",
|
||||
lp="292,105.82",
|
||||
pos="e,363.94,48.712 202.25,46.94 217.46,61.618 244.99,85.026 274,94.324 289.24,99.207 295.12,100.21 310,94.324 329.12,86.764 345.87,70.495 357.43,56.803"];
|
||||
1 -> 3 [label=<c>,
|
||||
lp="242,9.8246",
|
||||
pos="e,361.03,25.984 66.027,34.327 72.161,25.632 81.127,15.423 92,10.325 114.02,0 277.48,0.3418 312,7.3246 325.76,10.108 340.24,15.943 351.94,21.478"];
|
||||
0 -> 0 [label=<b<br/><font color="#5DA5DA">⓿</font>>,
|
||||
lp="190,172.33",
|
||||
pos="e,198.98,137.24 181.02,137.24 178.68,147.48 181.67,157.33 190,157.33 195.47,157.33 198.63,153.08 199.5,147.28"];
|
||||
2 -> 1 [label=<!a & !c<br/><font color="#5DA5DA">⓿</font>>,
|
||||
lp="123,35.324",
|
||||
pos="e,68.596,36.186 173.36,26.591 167.44,24.066 160.55,21.587 154,20.324 126.94,15.113 117.92,10.98 92,20.324 86.432,22.331 81.123,25.651 76.398,29.343"];
|
||||
2 -> 2 [label=<a & !c>,
|
||||
lp="190,77.824",
|
||||
pos="e,198.98,50.24 181.02,50.24 178.68,60.475 181.67,70.324 190,70.324 195.47,70.324 198.63,66.083 199.5,60.274"];
|
||||
2 -> 3 [label=<!a & c>,
|
||||
lp="294,105.83",
|
||||
pos="e,365.94,48.712 203.15,46.686 218.52,61.348 246.56,84.98 276,94.324 291.25,99.165 297.12,100.21 312,94.324 331.12,86.764 347.87,70.495 359.43,56.803"];
|
||||
4 [height=0.5,
|
||||
label=4,
|
||||
pos="292,34.162",
|
||||
pos="294,34.168",
|
||||
width=0.5];
|
||||
2 -> 4 [label="a & c",
|
||||
lp="240.5,41.824",
|
||||
pos="e,273.78,34.324 207.13,34.324 222.59,34.324 245.58,34.324 263.59,34.324"];
|
||||
3 -> 3 [label="1\\n{0}",
|
||||
lp="375,85.324",
|
||||
pos="e,382.03,50.988 367.97,50.988 366.41,60.949 368.75,70.324 375,70.324 379,70.324 381.4,66.475 382.2,61.092"];
|
||||
4 -> 3 [label="!a",
|
||||
lp="333.5,41.824",
|
||||
pos="e,356.85,34.324 310.18,34.324 320.81,34.324 334.69,34.324 346.8,34.324"];
|
||||
4 -> 4 [label=a,
|
||||
lp="292,77.824",
|
||||
pos="e,299.03,50.988 284.97,50.988 283.41,60.949 285.75,70.324 292,70.324 296,70.324 298.4,66.475 299.2,61.092"];
|
||||
2 -> 4 [label=<a & c>,
|
||||
lp="242,41.824",
|
||||
pos="e,275.95,34.324 208.3,34.324 224.08,34.324 247.64,34.324 265.91,34.324"];
|
||||
3 -> 3 [label=<1<br/><font color="#5DA5DA">⓿</font>>,
|
||||
lp="377,85.324",
|
||||
pos="e,384.03,50.989 369.97,50.989 368.41,60.949 370.75,70.324 377,70.324 381,70.324 383.4,66.477 384.2,61.093"];
|
||||
4 -> 3 [label=<!a>,
|
||||
lp="335.5,41.824",
|
||||
pos="e,358.85,34.324 312.18,34.324 322.81,34.324 336.69,34.324 348.8,34.324"];
|
||||
4 -> 4 [label=<a>,
|
||||
lp="294,77.824",
|
||||
pos="e,301.03,50.989 286.97,50.989 285.41,60.949 287.75,70.324 294,70.324 298,70.324 300.4,66.477 301.2,61.093"];
|
||||
}
|
||||
subgraph cluster_gv1 {
|
||||
graph [bb="",
|
||||
label="a U b",
|
||||
fontname=Lato,
|
||||
label=<a U b>,
|
||||
labelloc=t,
|
||||
lheight=0.21,
|
||||
lp="80.5,88.5",
|
||||
lwidth=0.43,
|
||||
lp="81.5,88.5",
|
||||
lwidth=0.47,
|
||||
rankdir=LR
|
||||
];
|
||||
node [height="",
|
||||
node [fillcolor="#ffffa0",
|
||||
fontname=Lato,
|
||||
height="",
|
||||
label="\\N",
|
||||
peripheries="",
|
||||
pos="",
|
||||
shape=circle,
|
||||
style="",
|
||||
style=filled,
|
||||
width=""
|
||||
];
|
||||
edge [label="",
|
||||
edge [fontname=Lato,
|
||||
label="",
|
||||
lp="",
|
||||
pos=""
|
||||
];
|
||||
I_gv1 [height=0.013889,
|
||||
label="",
|
||||
pos="261,156.16",
|
||||
pos="261,156.17",
|
||||
style=invis,
|
||||
width=0.013889];
|
||||
"1_gv1" [height=0.5,
|
||||
label=1,
|
||||
pos="316,156.16",
|
||||
pos="316,156.17",
|
||||
width=0.5];
|
||||
I_gv1 -> "1_gv1" [pos="e,297.94,156.16 261.15,156.16 262.67,156.16 275.1,156.16 287.63,156.16"];
|
||||
"1_gv1" -> "1_gv1" [label="a & !b",
|
||||
lp="316,199.66",
|
||||
pos="e,322.38,173.2 309.62,173.2 308.32,183.02 310.44,192.16 316,192.16 319.47,192.16 321.6,188.59 322.4,183.51"];
|
||||
I_gv1 -> "1_gv1" [pos="e,297.94,156.17 261.15,156.17 262.67,156.17 275.1,156.17 287.63,156.17"];
|
||||
"1_gv1" -> "1_gv1" [label=<a & !b>,
|
||||
lp="316,199.67",
|
||||
pos="e,322.38,173.21 309.62,173.21 308.32,183.03 310.44,192.17 316,192.17 319.47,192.17 321.6,188.6 322.4,183.52"];
|
||||
"0_gv1" [height=0.72222,
|
||||
label=0,
|
||||
peripheries=2,
|
||||
pos="399,156.16",
|
||||
pos="401,156.17",
|
||||
width=0.72222];
|
||||
"1_gv1" -> "0_gv1" [label=b,
|
||||
lp="355.5,163.66",
|
||||
pos="e,376.81,156.16 334.18,156.16 343.61,156.16 355.6,156.16 366.64,156.16"];
|
||||
"1_gv1" -> "0_gv1" [label=<b>,
|
||||
lp="356.5,163.67",
|
||||
pos="e,379,156.17 334.2,156.17 344.16,156.17 357,156.17 368.7,156.17"];
|
||||
"0_gv1" -> "0_gv1" [label=1,
|
||||
lp="399,203.66",
|
||||
pos="e,406.68,177.15 391.32,177.15 390.37,187.25 392.93,196.16 399,196.16 402.89,196.16 405.34,192.5 406.35,187.22"];
|
||||
lp="401,203.67",
|
||||
pos="e,409.01,176.75 392.99,176.75 391.89,187.01 394.55,196.17 401,196.17 405.13,196.17 407.71,192.41 408.74,187.01"];
|
||||
}
|
||||
}
|
||||
#+end_example
|
||||
|
|
@ -457,10 +476,14 @@ of Promela syntax.)
|
|||
The =--dot= option (which usually is the default) causes automata to be
|
||||
output in GraphViz's format.
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports both
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba '(Ga -> Gb) W c'
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports result
|
||||
SPOT_DOTEXTRA= ltl2tgba '(Ga -> Gb) W c' --dot=
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
|
|
@ -492,7 +515,7 @@ picture. For instance use =dot -Tpng= or =dot -Tpdf=.
|
|||
|
||||
#+NAME: oaut-dot1
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba '(Ga -> Gb) W c' | sed 's/\\/\\\\/'
|
||||
SPOT_DOTEXTRA= ltl2tgba '(Ga -> Gb) W c' --dot= | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: oaut-dot1
|
||||
|
|
@ -533,7 +556,14 @@ This output can be customized by passing optional characters to the
|
|||
of the default horizontal layout), =c= requests circle states, =s=
|
||||
causes strongly-connected components to be displayed, =n= causes the
|
||||
name (see below) of the automaton to be displayed, and =a= causes the
|
||||
acceptance condition to be shown as well.
|
||||
acceptance condition to be shown as well. Option =b= causes sets to
|
||||
be ouput as bullets (e.g., ⓿ instead of ={0}=); option =r= (for
|
||||
rainbow) causes sets to be displayed in different colors, while option
|
||||
=R= also uses colors, but it chooses them depending on whether a set
|
||||
is used with Fin-acceptance, Inf-acceptance, or both. Finally option
|
||||
=f(FONT)= is used to select a fontname: is is often necessary when =b=
|
||||
is used to ensure the characters ⓿, ❶, etc. are all selected from the
|
||||
same font.
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba --dot=vcsna '(Ga -> Gb) W c'
|
||||
|
|
@ -544,6 +574,7 @@ digraph G {
|
|||
label="(Gb | F!a) W c\nInf(0)"
|
||||
labelloc="t"
|
||||
node [shape="circle"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, height=0]
|
||||
I -> 1
|
||||
subgraph cluster_0 {
|
||||
|
|
@ -584,83 +615,50 @@ digraph G {
|
|||
|
||||
#+NAME: oaut-dot2
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba --dot=vcsna '(Ga -> Gb) W c' | sed 's/\\/\\\\/'
|
||||
SPOT_DOTEXTRA= ltl2tgba --dot=vcsna '(Ga -> Gb) W c' | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: oaut-dot2
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
label="Fin(2) & (Inf(0)&Inf(1))"
|
||||
label="(Gb | F!a) W c\\nInf(0)"
|
||||
labelloc="t"
|
||||
node [shape="circle"]
|
||||
I [label="", style=invis, width=0]
|
||||
I [label="", style=invis, height=0]
|
||||
I -> 1
|
||||
subgraph cluster_0 {
|
||||
color=grey
|
||||
label=""
|
||||
5 [label="5"]
|
||||
6 [label="6"]
|
||||
}
|
||||
subgraph cluster_1 {
|
||||
color=orange
|
||||
color=green
|
||||
label=""
|
||||
0 [label="0"]
|
||||
}
|
||||
subgraph cluster_1 {
|
||||
color=green
|
||||
label=""
|
||||
3 [label="3"]
|
||||
}
|
||||
subgraph cluster_2 {
|
||||
color=orange
|
||||
label=""
|
||||
9 [label="9"]
|
||||
10 [label="10"]
|
||||
}
|
||||
subgraph cluster_3 {
|
||||
color=green
|
||||
label=""
|
||||
8 [label="8"]
|
||||
}
|
||||
subgraph cluster_4 {
|
||||
color=green
|
||||
label=""
|
||||
7 [label="7"]
|
||||
}
|
||||
subgraph cluster_5 {
|
||||
color=black
|
||||
label=""
|
||||
2 [label="2"]
|
||||
}
|
||||
subgraph cluster_6 {
|
||||
color=red
|
||||
label=""
|
||||
4 [label="4"]
|
||||
}
|
||||
subgraph cluster_7 {
|
||||
subgraph cluster_3 {
|
||||
color=green
|
||||
label=""
|
||||
1 [label="1"]
|
||||
3 [label="3"]
|
||||
2 [label="2"]
|
||||
}
|
||||
0 -> 0 [label="a & b\\n{0,1,2}"]
|
||||
0 -> 0 [label="!a & !b\\n{2}"]
|
||||
0 -> 5 [label="a\\n{2}"]
|
||||
1 -> 4 [label="b"]
|
||||
1 -> 3 [label="a & !b"]
|
||||
2 -> 0 [label="a"]
|
||||
2 -> 7 [label="b"]
|
||||
3 -> 1 [label="a & b\\n{0,1}"]
|
||||
4 -> 4 [label="!b\\n{1,2}"]
|
||||
4 -> 2 [label="b"]
|
||||
5 -> 6 [label="1"]
|
||||
6 -> 5 [label="1"]
|
||||
7 -> 7 [label="!a & b\\n{0,1}"]
|
||||
7 -> 7 [label="a & b\\n{0,2}"]
|
||||
7 -> 8 [label="1"]
|
||||
8 -> 8 [label="!a & b\\n{0,2}"]
|
||||
8 -> 8 [label="a & b\\n{0,1}"]
|
||||
8 -> 9 [label="1"]
|
||||
9 -> 9 [label="!a & b\\n{0,2}"]
|
||||
9 -> 10 [label="a & b\\n{0,1}"]
|
||||
10 -> 9 [label="!a & b\\n{0,1}"]
|
||||
10 -> 10 [label="a & b\\n{0,2}"]
|
||||
0 -> 0 [label="b\\n{0}"]
|
||||
1 -> 0 [label="a & b & !c"]
|
||||
1 -> 1 [label="!a & !c\\n{0}"]
|
||||
1 -> 2 [label="a & !c"]
|
||||
1 -> 3 [label="c"]
|
||||
2 -> 1 [label="!a & !c\\n{0}"]
|
||||
2 -> 2 [label="a & !c"]
|
||||
2 -> 3 [label="!a & c"]
|
||||
2 -> 4 [label="a & c"]
|
||||
3 -> 3 [label="1\\n{0}"]
|
||||
4 -> 3 [label="!a"]
|
||||
4 -> 4 [label="a"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -686,7 +684,7 @@ Here is an example involving all colors:
|
|||
|
||||
#+NAME: oaut-dot3
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
autfilt --dot=cas <<EOF | sed 's/\\/\\\\/'
|
||||
SPOT_DOTEXTRA= autfilt --dot=cas <<EOF | sed 's/\\/\\\\/'
|
||||
HOA: v1
|
||||
States: 10
|
||||
Start: 1
|
||||
|
|
@ -803,6 +801,30 @@ $txt
|
|||
#+RESULTS:
|
||||
[[file:oaut-dot3.png]]
|
||||
|
||||
|
||||
The dot output can also be customized via two environment variables:
|
||||
- =SPOT_DOTDEFAULT= contains default arguments for the =--dot= option
|
||||
(for when it is used implicitly, or used as just =--dot= without
|
||||
argument). For instance after =export SPOT_DOTDEFAULT=vcsn=, using
|
||||
=--dot= is equivalent to =--dot=vcsn=. However using =--dot=xyz=
|
||||
(for any value of =xyz=, even empty) will ignore the
|
||||
=SPOT_DOTDEFAULT= variable. If the argument of =--dot= contains
|
||||
a dot character, then this dot is replaced by the contents of
|
||||
=SPOT_DOTDEFAULT=. So ~--dot=.a~ would be equivalent to =--dot=vcsna=
|
||||
with our example definition of =SPOT_DOTDEFAULT=.
|
||||
- =SPOT_DOTEXTRA= may contains an arbitrary string that will be emitted
|
||||
in the dot output before the first state. This can be used to modify
|
||||
any attribute. For instance (except for this page, where we had
|
||||
do demonstrate the various options of =--dot=, and a few pages where
|
||||
we show the =--dot= output verbatim) all the automata displayed in
|
||||
this documentation are generated with the following environment
|
||||
variables set:
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
export SPOT_DOTDEFAULT='brf(Lato)'
|
||||
export SPOT_DOTEXTRA='node[style=filled, fillcolor="#ffffa0"]'
|
||||
#+END
|
||||
|
||||
* Statistics
|
||||
|
||||
The =--stats= option takes format string parameter to specify what and
|
||||
|
|
@ -877,37 +899,18 @@ By default, =ltl2tgba= will use the input format as name. Other tools
|
|||
have no default name. This name can be changed using the =--name= option,
|
||||
that takes a format string similar to the one of =--stats=.
|
||||
|
||||
#+NAME: oaut-name
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba --name='TGBA for %f' --dot=n 'a U b'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
label="TGBA for a U b"
|
||||
labelloc="t"
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 1
|
||||
0 [label="0", peripheries=2]
|
||||
0 -> 0 [label="1"]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="b"]
|
||||
1 -> 1 [label="a & !b"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: oaut-name
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba --name='TGBA for %f' --dot=n 'a U b' | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: oaut-name
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
label="TGBA for a U b"
|
||||
labelloc="t"
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 1
|
||||
0 [label="0", peripheries=2]
|
||||
|
|
|
|||
|
|
@ -9,56 +9,52 @@ By default, it will generate a random TGBA with 10 states, no
|
|||
acceptance sets, and using a set of atomic proposition you have to
|
||||
supply.
|
||||
|
||||
#+NAME: randaut1
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut a b
|
||||
#+END_SRC
|
||||
|
||||
#+NAME: randaut1
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
randaut a b | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
#+RESULTS: randaut1
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0", peripheries=2]
|
||||
1 -> 2 [label="!a & !b"]
|
||||
1 -> 3 [label="!a & b"]
|
||||
2 [label="4", peripheries=2]
|
||||
2 -> 4 [label="a & b"]
|
||||
2 -> 5 [label="a & b"]
|
||||
2 -> 3 [label="a & b"]
|
||||
2 -> 6 [label="!a & b"]
|
||||
3 [label="2", peripheries=2]
|
||||
3 -> 3 [label="a & b"]
|
||||
3 -> 7 [label="!a & b"]
|
||||
3 -> 2 [label="!a & b"]
|
||||
3 -> 6 [label="!a & b"]
|
||||
4 [label="6", peripheries=2]
|
||||
4 -> 8 [label="!a & !b"]
|
||||
4 -> 6 [label="!a & !b"]
|
||||
4 -> 7 [label="a & b"]
|
||||
4 -> 9 [label="!a & b"]
|
||||
5 [label="5", peripheries=2]
|
||||
5 -> 2 [label="!a & b"]
|
||||
5 -> 10 [label="a & !b"]
|
||||
6 [label="3", peripheries=2]
|
||||
6 -> 3 [label="!a & !b"]
|
||||
6 -> 9 [label="!a & !b"]
|
||||
7 [label="7", peripheries=2]
|
||||
7 -> 9 [label="!a & b"]
|
||||
8 [label="1", peripheries=2]
|
||||
8 -> 1 [label="!a & b"]
|
||||
8 -> 6 [label="!a & !b"]
|
||||
9 [label="8", peripheries=2]
|
||||
9 -> 3 [label="a & b"]
|
||||
9 -> 10 [label="a & b"]
|
||||
9 -> 7 [label="a & !b"]
|
||||
9 -> 8 [label="!a & b"]
|
||||
10 [label="9", peripheries=2]
|
||||
10 -> 10 [label="a & !b"]
|
||||
10 -> 5 [label="a & !b"]
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 8 [label=<!a & !b>]
|
||||
0 -> 4 [label=<!a & !b>]
|
||||
1 [label="1"]
|
||||
1 -> 2 [label=<a & !b>]
|
||||
1 -> 7 [label=<!a & !b>]
|
||||
1 -> 4 [label=<!a & b>]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label=<!a & !b>]
|
||||
2 -> 0 [label=<a & !b>]
|
||||
2 -> 5 [label=<a & !b>]
|
||||
3 [label="3"]
|
||||
3 -> 6 [label=<!a & b>]
|
||||
4 [label="4"]
|
||||
4 -> 8 [label=<a & !b>]
|
||||
4 -> 2 [label=<!a & b>]
|
||||
4 -> 3 [label=<a & b>]
|
||||
4 -> 7 [label=<!a & b>]
|
||||
5 [label="5"]
|
||||
5 -> 9 [label=<!a & !b>]
|
||||
5 -> 3 [label=<a & !b>]
|
||||
5 -> 7 [label=<!a & !b>]
|
||||
6 [label="6"]
|
||||
6 -> 7 [label=<!a & !b>]
|
||||
6 -> 1 [label=<!a & b>]
|
||||
7 [label="7"]
|
||||
7 -> 3 [label=<!a & !b>]
|
||||
8 [label="8"]
|
||||
8 -> 8 [label=<!a & b>]
|
||||
9 [label="9"]
|
||||
9 -> 0 [label=<!a & b>]
|
||||
9 -> 6 [label=<!a & b>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -86,26 +82,27 @@ variance $(S-1)d(1-d)$.
|
|||
In particular =-d0= will cause all states to have 1 successors, and
|
||||
=-d1= will cause all states to be interconnected.
|
||||
|
||||
#+NAME: randaut2
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut -S3 -d0 2
|
||||
#+END_SRC
|
||||
|
||||
#+NAME: randaut2
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
randaut -S3 -d0 2 | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: randaut2
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0", peripheries=2]
|
||||
1 -> 2 [label="!p0 & !p1"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 3 [label="!p0 & p1"]
|
||||
3 [label="1", peripheries=2]
|
||||
3 -> 2 [label="p0 & p1"]
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 2 [label=<!p0 & !p1>]
|
||||
1 [label="1"]
|
||||
1 -> 1 [label=<!p0 & !p1>]
|
||||
2 [label="2"]
|
||||
2 -> 1 [label=<!p0 & !p1>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -115,32 +112,33 @@ $txt
|
|||
#+RESULTS:
|
||||
[[file:randaut2.png]]
|
||||
|
||||
#+NAME: randaut3
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut -S3 -d1 2
|
||||
#+END_SRC
|
||||
|
||||
#+NAME: randaut3
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
randaut -S3 -d1 2 | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: randaut3
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0", peripheries=2]
|
||||
1 -> 2 [label="!p0 & !p1"]
|
||||
1 -> 1 [label="!p0 & !p1"]
|
||||
1 -> 3 [label="p0 & p1"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="p0 & !p1"]
|
||||
2 -> 3 [label="p0 & !p1"]
|
||||
2 -> 1 [label="!p0 & !p1"]
|
||||
3 [label="1", peripheries=2]
|
||||
3 -> 1 [label="!p0 & !p1"]
|
||||
3 -> 3 [label="!p0 & !p1"]
|
||||
3 -> 2 [label="p0 & p1"]
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 2 [label=<!p0 & !p1>]
|
||||
0 -> 0 [label=<!p0 & !p1>]
|
||||
0 -> 1 [label=<!p0 & !p1>]
|
||||
1 [label="1"]
|
||||
1 -> 1 [label=<p0 & p1>]
|
||||
1 -> 2 [label=<p0 & !p1>]
|
||||
1 -> 0 [label=<p0 & !p1>]
|
||||
2 [label="2"]
|
||||
2 -> 1 [label=<!p0 & !p1>]
|
||||
2 -> 0 [label=<p0 & !p1>]
|
||||
2 -> 2 [label=<p0 & !p1>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -171,29 +169,29 @@ The generation of acceptance sets is controlled with the following three paramet
|
|||
In addition, =-B= (or =--ba=) is a shorthand for =-A1 --state-acc=.
|
||||
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut -S3 -d0.5 -A2 -a0.2 2
|
||||
#+END_SRC
|
||||
|
||||
#+NAME: randaut4
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
randaut -S3 -d0.5 -A2 -a0.2 2 | sed 's/\\/\\\\/'
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut -S3 -d0.5 -A3 -a0.5 2
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: randaut4
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0"]
|
||||
1 -> 2 [label="!p0 & !p1\\n{1}"]
|
||||
1 -> 3 [label="!p0 & p1"]
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 1 [label=<!p0 & !p1>]
|
||||
0 -> 0 [label=<!p0 & !p1<br/><font color="#FAA43A">❷</font>>]
|
||||
1 [label="1"]
|
||||
1 -> 2 [label=<!p0 & p1<br/><font color="#F17CB0">❶</font><font color="#FAA43A">❷</font>>]
|
||||
2 [label="2"]
|
||||
2 -> 1 [label="!p0 & !p1\\n{0}"]
|
||||
2 -> 2 [label="!p0 & !p1"]
|
||||
3 [label="1"]
|
||||
3 -> 2 [label="!p0 & p1\\n{1}"]
|
||||
3 -> 3 [label="!p0 & p1"]
|
||||
2 -> 2 [label=<!p0 & !p1<br/><font color="#5DA5DA">⓿</font>>]
|
||||
2 -> 1 [label=<p0 & !p1<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -204,29 +202,28 @@ $txt
|
|||
[[file:randaut4.png]]
|
||||
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut -S3 -d0.4 -B -a0.5 2
|
||||
#+END_SRC
|
||||
|
||||
#+NAME: randaut5
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
randaut -S3 -d0.4 -B -a0.5 2 | sed 's/\\/\\\\/'
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut -S3 -d0.4 -B -a0.7 2
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: randaut5
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0", peripheries=2]
|
||||
1 -> 2 [label="!p0 & !p1\\n{0}"]
|
||||
1 -> 1 [label="!p0 & p1\\n{0}"]
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 2 [label=<!p0 & !p1>]
|
||||
1 [label="1"]
|
||||
1 -> 2 [label=<!p0 & p1>]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 3 [label="!p0 & p1\\n{0}"]
|
||||
2 -> 1 [label="p0 & !p1\\n{0}"]
|
||||
3 [label="1"]
|
||||
3 -> 3 [label="p0 & !p1"]
|
||||
3 -> 1 [label="p0 & !p1"]
|
||||
2 -> 1 [label=<!p0 & !p1>]
|
||||
2 -> 0 [label=<p0 & !p1>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -250,31 +247,31 @@ Boolean formulas over the given atomic propositions, such that the
|
|||
sum of all these formulas is $\top$. The resulting automaton is
|
||||
therefore deterministic and complete.
|
||||
|
||||
#+NAME: randaut6
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
randaut -D -S3 -d0.6 -A2 -a0.5 2
|
||||
#+END_SRC
|
||||
|
||||
#+NAME: randaut6
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
randaut -D -S3 -d0.6 -A2 -a0.5 2 | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: randaut6
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0"]
|
||||
1 -> 2 [label="p0\\n{1}"]
|
||||
1 -> 3 [label="!p0\\n{0,1}"]
|
||||
2 [label="1"]
|
||||
2 -> 3 [label="!p0 & p1"]
|
||||
2 -> 1 [label="!p0 & !p1\\n{0}"]
|
||||
2 -> 2 [label="p0\\n{0,1}"]
|
||||
3 [label="2"]
|
||||
3 -> 3 [label="p0 & p1\\n{1}"]
|
||||
3 -> 1 [label="p0 & !p1\\n{0}"]
|
||||
3 -> 2 [label="!p0"]
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 1 [label=<p0>]
|
||||
0 -> 2 [label=<!p0>]
|
||||
1 [label="1"]
|
||||
1 -> 2 [label=<p0<br/><font color="#F17CB0">❶</font>>]
|
||||
1 -> 0 [label=<!p0<br/><font color="#5DA5DA">⓿</font>>]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label=<!p0 & p1<br/><font color="#5DA5DA">⓿</font>>]
|
||||
2 -> 0 [label=<!p0 & !p1<br/><font color="#F17CB0">❶</font>>]
|
||||
2 -> 1 [label=<p0<br/><font color="#5DA5DA">⓿</font>>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
|
|||
|
|
@ -96,6 +96,7 @@ ltl2tgba -D -x sat-minimize "GF(a <-> XXb)" --stats='states=%s, det=%d'
|
|||
|
||||
We can draw it:
|
||||
|
||||
#+NAME: gfaexxb3
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -D -x sat-minimize "GF(a <-> XXb)"
|
||||
#+END_SRC
|
||||
|
|
@ -103,57 +104,32 @@ ltl2tgba -D -x sat-minimize "GF(a <-> XXb)"
|
|||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 1 [label="!b\n{0}"]
|
||||
0 -> 1 [label="a & b"]
|
||||
0 -> 2 [label="!a & b"]
|
||||
0 -> 1 [label=<!a & !b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
0 -> 2 [label=<!a & b>]
|
||||
0 -> 3 [label=<a & b>]
|
||||
0 -> 3 [label=<a & !b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
1 [label="1"]
|
||||
1 -> 1 [label="a & b\n{0}"]
|
||||
1 -> 1 [label="a & !b"]
|
||||
1 -> 2 [label="!a & !b"]
|
||||
1 -> 3 [label="!a & b\n{0}"]
|
||||
1 -> 0 [label=<a & b>]
|
||||
1 -> 0 [label=<a & !b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
1 -> 1 [label=<!a & b>]
|
||||
1 -> 1 [label=<!a & !b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a & !b"]
|
||||
2 -> 1 [label="b\n{0}"]
|
||||
2 -> 3 [label="!a & !b"]
|
||||
2 -> 0 [label=<a & !b>]
|
||||
2 -> 1 [label=<!a & b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
2 -> 1 [label=<!a & !b>]
|
||||
2 -> 3 [label=<a & b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
3 [label="3"]
|
||||
3 -> 0 [label="a & b"]
|
||||
3 -> 0 [label="a & !b\n{0}"]
|
||||
3 -> 3 [label="!a & b"]
|
||||
3 -> 3 [label="!a & !b\n{0}"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: gfaexxb3
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -D -x sat-minimize "GF(a <-> XXb)" | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
#+RESULTS: gfaexxb3
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 1 [label="!b\\n{0}"]
|
||||
0 -> 1 [label="a & b"]
|
||||
0 -> 2 [label="!a & b"]
|
||||
1 [label="1"]
|
||||
1 -> 1 [label="a & b\\n{0}"]
|
||||
1 -> 1 [label="a & !b"]
|
||||
1 -> 2 [label="!a & !b"]
|
||||
1 -> 3 [label="!a & b\\n{0}"]
|
||||
2 [label="2"]
|
||||
2 -> 0 [label="a & !b"]
|
||||
2 -> 1 [label="b\\n{0}"]
|
||||
2 -> 3 [label="!a & !b"]
|
||||
3 [label="3"]
|
||||
3 -> 0 [label="a & b"]
|
||||
3 -> 0 [label="a & !b\\n{0}"]
|
||||
3 -> 3 [label="!a & b"]
|
||||
3 -> 3 [label="!a & !b\\n{0}"]
|
||||
3 -> 2 [label=<!a & b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
3 -> 2 [label=<!a & !b>]
|
||||
3 -> 3 [label=<a & b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
3 -> 3 [label=<a & !b>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -168,82 +144,45 @@ acceptance. If we want a traditional Büchi automaton, with
|
|||
state-based acceptance, we only need to add the =-B= option. The
|
||||
result will of course be slightly bigger.
|
||||
|
||||
#+NAME: gfaexxb4
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
ltl2tgba -BD -x sat-minimize "GF(a <-> XXb)"
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 0 [label="!a & b"]
|
||||
0 -> 1 [label="!a & !b"]
|
||||
0 -> 2 [label="a & !b"]
|
||||
0 -> 3 [label="a & b"]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="!a & b\n{0}"]
|
||||
1 -> 2 [label="a & !b\n{0}"]
|
||||
1 -> 3 [label="a & b\n{0}"]
|
||||
1 -> 4 [label="!a & !b\n{0}"]
|
||||
2 [label="2"]
|
||||
2 -> 4 [label="!a\n{0}"]
|
||||
2 -> 5 [label="a\n{0}"]
|
||||
3 [label="3"]
|
||||
3 -> 1 [label="!a & !b"]
|
||||
3 -> 2 [label="a & !b"]
|
||||
3 -> 4 [label="!a & b"]
|
||||
3 -> 5 [label="a & b"]
|
||||
4 [label="4"]
|
||||
4 -> 0 [label="!a & !b"]
|
||||
4 -> 1 [label="!a & b"]
|
||||
4 -> 2 [label="a & b"]
|
||||
4 -> 3 [label="a & !b"]
|
||||
5 [label="5"]
|
||||
5 -> 1 [label="b"]
|
||||
5 -> 4 [label="!a & !b"]
|
||||
5 -> 5 [label="a & !b"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: gfaexxb4
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -BD -x sat-minimize "GF(a <-> XXb)" | sed 's/\\/\\\\/'
|
||||
#+END_SRC
|
||||
#+RESULTS: gfaexxb4
|
||||
#+begin_example
|
||||
digraph G {
|
||||
rankdir=LR
|
||||
fontname="Lato"
|
||||
node [fontname="Lato"]
|
||||
edge [fontname="Lato"]
|
||||
node[style=filled, fillcolor="#ffffa0"]
|
||||
I [label="", style=invis, width=0]
|
||||
I -> 0
|
||||
0 [label="0"]
|
||||
0 -> 0 [label="!a & b"]
|
||||
0 -> 1 [label="!a & !b"]
|
||||
0 -> 2 [label="a & !b"]
|
||||
0 -> 3 [label="a & b"]
|
||||
0 -> 0 [label=<!a & b>]
|
||||
0 -> 1 [label=<!b>]
|
||||
0 -> 2 [label=<a & b>]
|
||||
1 [label="1"]
|
||||
1 -> 0 [label="!a & b\\n{0}"]
|
||||
1 -> 2 [label="a & !b\\n{0}"]
|
||||
1 -> 3 [label="a & b\\n{0}"]
|
||||
1 -> 4 [label="!a & !b\\n{0}"]
|
||||
1 -> 4 [label=<!a<br/><font color="#5DA5DA">⓿</font>>]
|
||||
1 -> 5 [label=<a<br/><font color="#5DA5DA">⓿</font>>]
|
||||
2 [label="2"]
|
||||
2 -> 4 [label="!a\\n{0}"]
|
||||
2 -> 5 [label="a\\n{0}"]
|
||||
2 -> 1 [label=<!b>]
|
||||
2 -> 4 [label=<!a & b>]
|
||||
2 -> 5 [label=<a & b>]
|
||||
3 [label="3"]
|
||||
3 -> 1 [label="!a & !b"]
|
||||
3 -> 2 [label="a & !b"]
|
||||
3 -> 4 [label="!a & b"]
|
||||
3 -> 5 [label="a & b"]
|
||||
3 -> 0 [label=<!a<br/><font color="#5DA5DA">⓿</font>>]
|
||||
3 -> 1 [label=<a & !b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
3 -> 2 [label=<a & b<br/><font color="#5DA5DA">⓿</font>>]
|
||||
4 [label="4"]
|
||||
4 -> 0 [label="!a & !b"]
|
||||
4 -> 1 [label="!a & b"]
|
||||
4 -> 2 [label="a & b"]
|
||||
4 -> 3 [label="a & !b"]
|
||||
4 -> 0 [label=<!a & !b>]
|
||||
4 -> 1 [label=<a & b>]
|
||||
4 -> 2 [label=<a & !b>]
|
||||
4 -> 3 [label=<!a & b>]
|
||||
5 [label="5"]
|
||||
5 -> 1 [label="b"]
|
||||
5 -> 4 [label="!a & !b"]
|
||||
5 -> 5 [label="a & !b"]
|
||||
5 -> 1 [label=<a & b>]
|
||||
5 -> 3 [label=<!a & b>]
|
||||
5 -> 4 [label=<!a & !b>]
|
||||
5 -> 5 [label=<a & !b>]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue