adjust documentation for the merge of the dstar parser
* NEWS: Mention the changes. * doc/org/autfilt.org, doc/org/dstar2tgba.org, doc/org/ltlcross.org, doc/org/tools.org, doc/org/tut20.org, src/bin/man/dstar2tgba.x, src/bin/man/ltlcross.x: Adjust documentation. * src/bin/common_trans.cc: Use %O instead of %D, but keep %D hidden for backward compatibility.
This commit is contained in:
Alexandre Duret-Lutz
parent
c59e994a2c
commit
17a18f2890
9 changed files with 357 additions and 173 deletions
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@ -3,12 +3,17 @@
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#+SETUPFILE: setup.org
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#+HTML_LINK_UP: tools.html
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This tool converts deterministic Rabin and Streett automata, presented
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in [[http://www.ltl2dstar.de/docs/ltl2dstar.html][the format output by =ltl2dstar=]], into Büchi automata.
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This tool converts automata into transition-based generalized Büchi
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automata, a.k.a., TGBA.
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In earlier version (before Spot 1.99.4) =dstar2tgba= was only able to
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read automata written in [[http://www.ltl2dstar.de/docs/ltl2dstar.html][the format output by =ltl2dstar=]], hence its
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name. However nowadays it can read automata in any of the supported
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formats ([[file:hoa.org][HOA]], LBTT's format, ltl2dstar's format, and never claims).
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It's usage is almost similar to [[file:ltl2tgba.org][=ltl2tgba=]] except that instead of
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supplying a formula to translate, you should specify a filename
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containing the deterministic Rabin or Streett automaton to convert.
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containing the automaton to convert.
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* Two quick examples
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@ -18,18 +23,18 @@ Here are some brief examples before we discuss the behavior of
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** From Rabin to Büchi
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The following command instructs =ltl2dstar= to:
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1. run =ltl2tgba -sD= to build a Büchi automaton for =Fa & GFb=, and then
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1. run =ltl2tgba -Ds= to build a Büchi automaton for =(a U b) & GFb=, and then
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2. convert that Büchi automaton into a deterministic Rabin automaton
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(DRA) stored in =fagfb=.
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Additionally we use =ltlfilt= to convert our formula to the
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prefix format used by =ltl2dstar=.
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#+BEGIN_SRC sh :results silent :exports both
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ltlfilt -f 'Fa & GFb' -l | ltl2dstar --ltl2nba=spin:ltl2tgba@-sD - fagfb
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ltlfilt -f '(a U b) & GFb' -l | ltl2dstar --ltl2nba=spin:ltl2tgba@-Ds - fagfb
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#+END_SRC
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By looking at the file =fagfb= you can see the =ltl2dsar= actually
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produced a 3-state DRA:
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produced a 4-state DRA:
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#+BEGIN_SRC sh :results verbatim :exports both
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cat fagfb
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@ -38,64 +43,87 @@ cat fagfb
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#+begin_example
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DRA v2 explicit
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Comment: "Safra[NBA=3]"
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States: 3
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States: 4
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Acceptance-Pairs: 1
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Start: 1
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Start: 2
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AP: 2 "a" "b"
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---
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State: 0
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Acc-Sig: +0
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2
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2
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3
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3
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0
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0
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State: 1
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Acc-Sig:
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Acc-Sig: -0
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1
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1
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1
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0
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1
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0
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State: 2
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Acc-Sig:
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1
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2
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2
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0
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0
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State: 3
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Acc-Sig:
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3
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3
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0
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0
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#+end_example
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Let's display this automaton with =autfilt=:
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#+NAME: fagfb
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#+BEGIN_SRC sh :results verbatim :exports code
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autfilt fagfb --dot=.a
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#+END_SRC
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#+RESULTS: fagfb
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#+begin_example
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digraph G {
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rankdir=LR
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label=<Fin(<font color="#5DA5DA">⓿</font>) & Inf(<font color="#F17CB0">❶</font>)>
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labelloc="t"
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node [shape="circle"]
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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"] edge[arrowhead=vee, arrowsize=.7]
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I [label="", style=invis, width=0]
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I -> 2
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0 [label=<0<br/><font color="#F17CB0">❶</font>>]
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0 -> 0 [label=<b>]
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0 -> 3 [label=<!b>]
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1 [label=<1<br/><font color="#5DA5DA">⓿</font>>]
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1 -> 1 [label=<1>]
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2 [label=<2>]
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2 -> 0 [label=<b>]
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2 -> 1 [label=<!a & !b>]
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2 -> 2 [label=<a & !b>]
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3 [label=<3>]
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3 -> 0 [label=<b>]
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3 -> 3 [label=<!b>]
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}
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#+end_example
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#+BEGIN_SRC dot :file fagfb.png :cmdline -Tpng :var txt=fagfb :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:fagfb.png]]
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We used =--dot=a= to display Spot's representation of the acceptance
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condition (which uses the same convention as in the [[file:hoa.org][HOA format]]). The
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extra dot is because we use some [[file:oaut.org][environment variables]] to produce a
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more colorful output by default in these pages.
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=dstar2tgba= can now be used to convert this DRA into a TGBA, a BA, or
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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://www.graphviz.org/][GraphViz]]'s format:
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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 -> 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 -> 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 (note that in this documentation
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we use some [[file:oaut.org][environment variables]] to produce a more colorful
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output by default):
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For instance here is the conversion to a Büchi automaton (=-B=):
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#+NAME: fagfb2ba
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#+BEGIN_SRC sh :results verbatim :exports code
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@ -105,19 +133,20 @@ dstar2tgba -B fagfb
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#+begin_example
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digraph G {
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rankdir=LR
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node [shape="circle"]
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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"] edge[arrowhead=vee, arrowsize=.7]
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I [label="", style=invis, width=0]
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I -> 1
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0 [label=<0<br/><font color="#5DA5DA">⓿</font>>]
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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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1 [label="1"]
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1 -> 0 [label=<b>]
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1 -> 1 [label=<a & !b>]
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2 [label="2"]
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2 -> 0 [label=<b>]
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2 -> 2 [label=<!b>]
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}
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@ -129,7 +158,11 @@ $txt
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#+RESULTS:
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[[file:fagfb2ba.png]]
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But we could as well require the output to be output as a never claim for Spin (option =-s=):
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Note that by default the output is not complete. Use =-C= if you want
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a complete automaton.
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But we could as well require the output as a never claim for Spin (option =-s=):
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#+BEGIN_SRC sh :results verbatim :exports both
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dstar2tgba -s fagfb
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@ -139,18 +172,18 @@ dstar2tgba -s fagfb
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never {
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T0_init:
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if
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:: ((!(a))) -> goto T0_init
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:: ((a)) -> goto accept_S2
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:: ((b)) -> goto accept_S0
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:: ((a) && (!(b))) -> goto T0_init
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fi;
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accept_S2:
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accept_S0:
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if
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:: ((b)) -> goto accept_S2
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:: ((!(b))) -> goto T0_S3
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:: ((b)) -> goto accept_S0
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:: ((!(b))) -> goto T0_S2
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fi;
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T0_S3:
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T0_S2:
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if
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:: ((b)) -> goto accept_S2
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:: ((!(b))) -> goto T0_S3
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:: ((b)) -> goto accept_S0
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:: ((!(b))) -> goto T0_S2
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fi;
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}
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#+end_example
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@ -160,50 +193,62 @@ T0_S3:
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:CUSTOM_ID: streett_to_tgba_example
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:END:
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Here is the translation of =GFa & GFb= to a 4-state Streett automaton:
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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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#+NAME: gfafgb
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#+BEGIN_SRC sh :results verbatim :exports code
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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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autfilt --dot=.a gfagfb
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#+END_SRC
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#+RESULTS:
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#+RESULTS: gfafgb
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#+begin_example
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DSA v2 explicit
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Comment: "Streett{Union{Safra[NBA=2],Safra[NBA=2]}}"
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States: 4
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Acceptance-Pairs: 2
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Start: 0
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AP: 2 "a" "b"
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---
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State: 0
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Acc-Sig: -0 -1
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3
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2
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1
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0
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State: 1
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Acc-Sig: +0 -1
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3
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2
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1
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0
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State: 2
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Acc-Sig: -0 +1
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3
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2
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1
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0
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State: 3
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Acc-Sig: +0 +1
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3
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2
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1
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0
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digraph G {
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rankdir=LR
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label=<(Fin(<font color="#5DA5DA">⓿</font>) | Inf(<font color="#F17CB0">❶</font>)) & (Fin(<font color="#FAA43A">❷</font>) | Inf(<font color="#B276B2">❸</font>))>
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labelloc="t"
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node [shape="circle"]
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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"] edge[arrowhead=vee, arrowsize=.7]
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I [label="", style=invis, width=0]
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I -> 0
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0 [label=<0<br/><font color="#F17CB0">❶</font><font color="#B276B2">❸</font>>]
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0 -> 0 [label=<a & b>]
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0 -> 1 [label=<!a & b>]
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0 -> 2 [label=<a & !b>]
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0 -> 3 [label=<!a & !b>]
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1 [label=<1<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
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1 -> 0 [label=<a & b>]
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1 -> 1 [label=<!a & b>]
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1 -> 2 [label=<a & !b>]
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1 -> 3 [label=<!a & !b>]
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2 [label=<2<br/><font color="#F17CB0">❶</font><font color="#FAA43A">❷</font>>]
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2 -> 0 [label=<a & b>]
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2 -> 1 [label=<!a & b>]
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2 -> 2 [label=<a & !b>]
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2 -> 3 [label=<!a & !b>]
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3 [label=<3<br/><font color="#5DA5DA">⓿</font><font color="#FAA43A">❷</font>>]
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3 -> 0 [label=<a & b>]
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3 -> 1 [label=<!a & b>]
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3 -> 2 [label=<a & !b>]
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3 -> 3 [label=<!a & !b>]
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}
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#+end_example
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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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#+BEGIN_SRC dot :file gfafgb.png :cmdline -Tpng :var txt=gfafgb :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:gfafgb.png]]
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And now its conversion by =dstar2tgba= to a 4-state TGBA.
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We don't pass any option to =dstar2tgba= because converting to TGBA is
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the default:
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#+NAME: gfagfb2ba
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#+BEGIN_SRC sh :results verbatim :exports code
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@ -213,6 +258,7 @@ dstar2tgba gfagfb
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#+begin_example
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digraph G {
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rankdir=LR
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node [shape="circle"]
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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@ -220,12 +266,25 @@ digraph G {
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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 -> 0 [label=<a & b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
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0 -> 1 [label=<!a & b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
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0 -> 2 [label=<a & !b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
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0 -> 3 [label=<!a & !b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
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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<br/><font color="#5DA5DA">⓿</font>>]
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1 -> 0 [label=<a & b<br/><font color="#F17CB0">❶</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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1 -> 2 [label=<a & !b<br/><font color="#F17CB0">❶</font>>]
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1 -> 3 [label=<!a & !b<br/><font color="#F17CB0">❶</font>>]
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2 [label="2"]
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2 -> 0 [label=<a & b<br/><font color="#5DA5DA">⓿</font>>]
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2 -> 1 [label=<!a & b<br/><font color="#5DA5DA">⓿</font>>]
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2 -> 2 [label=<a & !b<br/><font color="#5DA5DA">⓿</font>>]
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2 -> 3 [label=<!a & !b<br/><font color="#5DA5DA">⓿</font>>]
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3 [label="3"]
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3 -> 0 [label=<a & b>]
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3 -> 1 [label=<!a & b>]
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3 -> 2 [label=<a & !b>]
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3 -> 3 [label=<!a & !b>]
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}
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#+end_example
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@ -235,20 +294,25 @@ $txt
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#+RESULTS:
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[[file:gfagfb2ba.png]]
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(Obviously the resulting automaton could be simplified further, by
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starting with the second state right away.)
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Obviously the resulting automaton could be simplified further, as the
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minimal TGBA for this formula has a single state. (Patches
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welcome...)
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* Details
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** General behavior
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The =dstar2tgba= tool implement a 4-step process:
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The =dstar2tgba= tool implements a 4-step process:
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1. read the DRA/DSA
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1. read the automaton
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2. convert it into TGBA
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3. postprocess the resulting TGBA (simplifying the automaton, a degeneralizing it into a BA or Monitor if requested)
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4. output the resulting automaton
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BTW, the above scenario is also exactly what you can with [[file:autfilt.org][=autfilt=]] if
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you run it as =autfilt --tgba --high --small=. (This is true only since version
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1.99.4, since both tools can now read the same file formats.)
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** Controlling output
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The last two steps are shared with =ltl2tgba= and use the same options.
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@ -301,18 +365,35 @@ dstar2tgba --help | sed -n '/Output format:/,/^$/p' | sed '1d;$d'
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#+begin_example
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-8, --utf8 enable UTF-8 characters in output (ignored with
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--lbtt or --spin)
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--dot[=c|h|n|N|s|t|v] GraphViz's format (default). Add letters to chose
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(c) circular nodes, (h) horizontal layout, (v)
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vertical layout, (n) with name, (N) without name,
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(s) with SCCs, (t) always transition-based
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acceptance.
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-H, --hoaf[=s|t|m|l] Output the automaton in HOA format. Add letters
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to select (s) state-based acceptance, (t)
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transition-based acceptance, (m) mixed acceptance,
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(l) single-line output
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--check[=PROP] test for the additional property PROP and output
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the result in the HOA format (implies -H). PROP
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may be any prefix of 'all' (default),
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||||
'unambiguous', or 'stutter-invariant'.
|
||||
--dot[=1|a|b|B|c|e|f(FONT)|h|n|N|o|r|R|s|t|v]
|
||||
GraphViz's format (default). Add letters for (1)
|
||||
force numbered states, (a) acceptance display, (b)
|
||||
acceptance sets as bullets, (B) bullets except for
|
||||
Büchi/co-Büchi automata, (c) force circular
|
||||
nodes, (e) force elliptic nodes, (f(FONT)) use
|
||||
FONT, (h) horizontal layout, (v) vertical layout,
|
||||
(n) with name, (N) without name, (o) ordered
|
||||
transitions, (r) rainbow colors for acceptance
|
||||
sets, (R) color acceptance sets 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
|
||||
-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
|
||||
states
|
||||
|
|
@ -358,7 +439,7 @@ done
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
(b | Fa) R Fc
|
||||
DRA: 9st.; BA: 6st.; det.? 1; complete? 1
|
||||
DRA: 9st.; BA: 9st.; det.? 1; complete? 1
|
||||
Ga U (Gc R (!a | Gc))
|
||||
DRA: 7st.; BA: 7st.; det.? 0; complete? 0
|
||||
GFc
|
||||
|
|
@ -368,7 +449,7 @@ GFc
|
|||
Xc R (G!c R (b | G!c))
|
||||
DRA: 4st.; BA: 2st.; det.? 1; complete? 0
|
||||
c & G(b | F(a & c))
|
||||
DRA: 5st.; BA: 3st.; det.? 1; complete? 0
|
||||
DRA: 4st.; BA: 3st.; det.? 1; complete? 0
|
||||
XXFc
|
||||
DRA: 4st.; BA: 4st.; det.? 1; complete? 1
|
||||
XFc | Gb
|
||||
|
|
@ -388,11 +469,46 @@ a difference of one state (the so called "sink" state).
|
|||
You can instruct =dstar2tgba= to output a complete automaton using the
|
||||
=--complete= option (or =-C= for short).
|
||||
|
||||
** Conversion from Rabin and Streett to TGBA
|
||||
** Conversion of various acceptance conditions to TGBA and BA
|
||||
|
||||
The algorithms used to convert Rabin and Streett into TGBA/BA are different.
|
||||
Spot implements several acceptance conversion algorithms.
|
||||
There is one generic cases, with some specialized variants.
|
||||
|
||||
*** Rabin to BA
|
||||
*** Generic case
|
||||
|
||||
The most generic one, called =remove_fin()= in Spot, takes an
|
||||
automaton with any acceptance condition, and as its name suggests, it
|
||||
removes all the =Fin(x)= from the acceptance condition: the output is
|
||||
an automaton whose acceptance conditions is a Boolean combination of
|
||||
=Inf(x)= acceptance primitive. (Such automata with Fin-less
|
||||
acceptance can be easily tested for emptiness using SCC-based
|
||||
emptiness checks.) This algorithm works by fist converting the
|
||||
acceptance conditions into disjunctive normal form, and then removing
|
||||
any =Fin(x)= acceptance by adding non-deterministic jumps into clones
|
||||
of the SCCs that intersect set =x=. This is done with a few tricks
|
||||
that limits the numbers of clones, and that ensure that the resulting
|
||||
automaton uses /at most/ one extra acceptance sets. This algorithm is
|
||||
not readily available from =dstar2tgba=, but [[file:autfilt.org][=autfilt=]] has an option
|
||||
=--remove-fin= if you need it.
|
||||
|
||||
From an automaton with Fin-less acceptance, one can obtain a TGBA
|
||||
without changing the transitions structure: take the Fin-less
|
||||
acceptance, transform it into conjunctive normal form (CNF), and
|
||||
create one new Fin-accepting set for each conjunct of the CNF. The
|
||||
combination of these two algorithms is implemented by the
|
||||
=to_generalized_buchi()= function in Spot.
|
||||
|
||||
Finally a TGBA can easily be converted into a BA with classical
|
||||
degeneralization algorithms (our version of that includes several
|
||||
SCC-based optimizations described in our [[https://www.lrde.epita.fr/~adl/dl/adl/babiak.13.spin.pdf][SPIN'13 paper]]).
|
||||
|
||||
This generalized case is specialized for two types of acceptances that
|
||||
are common (Rabin and Streett).
|
||||
|
||||
*** State-based Rabin to BA
|
||||
|
||||
For state-based Rabin automata, and dedicated conversion to BA is
|
||||
used.
|
||||
|
||||
The conversion implemented is a variation of Krishnan et al.'s
|
||||
"Deterministic ω-Automata vis-a-vis Deterministic Büchi Automata"
|
||||
|
|
@ -402,14 +518,21 @@ an automaton exist. The surprising result is that when a DRA is
|
|||
DBA-realizable, a DBA can be obtained from the DRA without changing
|
||||
its transition structure.
|
||||
|
||||
Spot implements a slight refinement to the above technique: any DRA
|
||||
will be converted into a BA, and the determinism will be conserved
|
||||
only in strongly connected components where determinism can be
|
||||
conserved.
|
||||
Spot implements a slight refinement to the above technique by doing it
|
||||
SCC-wise: any DRA will be converted into a BA, and the determinism
|
||||
will be conserved only for strongly connected components where
|
||||
determinism can be conserved. (If some SCC is not DBA-realizable, it
|
||||
will be cloned into several deterministic SCC, but the jumps between
|
||||
these SCCs will be nondeterministic.)
|
||||
|
||||
This specialized conversion is built in the =remove_fin()= procedure
|
||||
described above.
|
||||
|
||||
*** Streett to TGBA
|
||||
|
||||
Streett automata are converted into non-deterministic TGBA.
|
||||
Streett acceptance have a specialized conversion into non-deterministic TGBA.
|
||||
This improved conversion is automatically used by =to_generalized_buchi()=.
|
||||
|
||||
When a Streett automaton uses multiple acceptance pairs, we use
|
||||
generalized acceptance conditions in the TGBA to limit the combinatorial
|
||||
explosion.
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue