org: Update results to new output
The dotty output changed to be horizontal, and also the acceptance sets are now numbers. * doc/org/dstar2tgba.org, doc/org/ltl2tgba.org, doc/org/ltl2tgta.org, doc/org/satmin.org: Adjust these four.
This commit is contained in:
Alexandre Duret-Lutz
parent
f88020035c
commit
f9029858c4
4 changed files with 599 additions and 490 deletions
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@ -74,17 +74,18 @@ dstar2tgba -B fagfb
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#+RESULTS:
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#+begin_example
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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="1"]
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1 -> 2 [label="a\n"]
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1 -> 1 [label="!a\n"]
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2 [label="2", peripheries=2]
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2 -> 2 [label="b\n{Acc[1]}"]
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2 -> 3 [label="!b\n{Acc[1]}"]
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3 [label="3"]
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3 -> 2 [label="b\n"]
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3 -> 3 [label="!b\n"]
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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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2 [label="2"]
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2 -> 1 [label="b"]
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2 -> 2 [label="!b"]
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}
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#+end_example
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@ -97,17 +98,18 @@ dstar2tgba -B fagfb | sed 's/\\/\\\\/'
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#+RESULTS: fagfb2ba
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#+begin_example
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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="1"]
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1 -> 2 [label="a\\n"]
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1 -> 1 [label="!a\\n"]
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2 [label="2", peripheries=2]
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2 -> 2 [label="b\\n{Acc[1]}"]
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2 -> 3 [label="!b\\n{Acc[1]}"]
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3 [label="3"]
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3 -> 2 [label="b\\n"]
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3 -> 3 [label="!b\\n"]
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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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2 [label="2"]
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2 -> 1 [label="b"]
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2 -> 2 [label="!b"]
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}
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#+end_example
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@ -127,8 +129,8 @@ 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 accept_S2
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:: ((!(a))) -> goto T0_init
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:: ((a)) -> goto accept_S2
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fi;
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accept_S2:
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if
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@ -199,15 +201,16 @@ dstar2tgba gfagfb
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#+RESULTS:
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#+begin_example
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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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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 -> 2 [label="1\n"]
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2 [label="2"]
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2 -> 2 [label="a & b\n{Acc[\"1\"], Acc[\"0\"]}"]
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2 -> 2 [label="b & !a\n{Acc[\"1\"]}"]
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2 -> 2 [label="a & !b\n{Acc[\"0\"]}"]
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2 -> 2 [label="!a & !b\n"]
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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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@ -218,15 +221,16 @@ dstar2tgba gfagfb | sed 's/\\/\\\\/g'
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#+RESULTS: gfagfb2ba
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#+begin_example
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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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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 -> 2 [label="1\\n"]
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2 [label="2"]
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2 -> 2 [label="a & b\\n{Acc[\\"1\\"], Acc[\\"0\\"]}"]
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2 -> 2 [label="b & !a\\n{Acc[\\"1\\"]}"]
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2 -> 2 [label="a & !b\\n{Acc[\\"0\\"]}"]
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2 -> 2 [label="!a & !b\\n"]
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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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@ -293,25 +297,36 @@ dstar2tgba --help | sed -n '/Optimization level:/,/^$/p' | sed '1d;$d'
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For instance using =-a --low= will skip any optional post-processing,
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should you find =dstar2tgba= too slow.
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Finally, the output format can be changed with the following options:
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Finally, the output format can be changed with the following
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[[file:oaout.org][common ouput options]]:
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#+BEGIN_SRC sh :results verbatim :exports results
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dstar2tgba --help | sed -n '/Output format:/,/^$/p' | sed '1d;$d'
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#+END_SRC
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#+RESULTS:
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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 GraphViz's format (default)
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: --lbtt[=t] LBTT's format (add =t to force transition-based
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: acceptance even on Büchi automata)
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: -s, --spin Spin neverclaim (implies --ba)
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: --spot SPOT's format
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: --stats=FORMAT output statistics about the automaton
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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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--lbtt[=t] LBTT's format (add =t to force transition-based
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acceptance even on Büchi automata)
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--name=FORMAT set the name of the output automaton
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-s, --spin Spin neverclaim (implies --ba)
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--spot SPOT's format
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--stats=FORMAT output statistics about the automaton
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#+end_example
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The =--stats= options can output statistics about the input and the
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output automaton, so it can be useful to search for particular
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pattern.
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For instance here is a complex command that will
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1. generate an infinite stream of random LTL formulas with [[file:randltl.org][=randltl=]],
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@ -333,7 +348,7 @@ output (Büchi) automaton, =%d=, whether the output automaton is
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deterministic, and =%p= whether the automaton is complete.
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#+BEGIN_SRC sh :results verbatim :exports both
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randltl -n -1 --tree-size=10..15 a b c |
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randltl -n -1 --tree-size=10..14 a b c |
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ltlfilt --remove-wm -r -u --size-min=3 |
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head -n 10 |
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while read f; do
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@ -346,26 +361,26 @@ done
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#+RESULTS:
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#+begin_example
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F(a | !b)
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DRA: 2st.; BA: 2st.; det.? 1; complete? 1
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Fa | (Xc U (c & Xc))
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DRA: 5st.; BA: 5st.; det.? 1; complete? 1
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X(((!b & XGc) | (b & XF!c)) U (!a & ((!b & XGc) | (b & XF!c))))
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DRA: 8st.; BA: 7st.; det.? 1; complete? 0
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!b | !a
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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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F!a
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DRA: 2st.; BA: 2st.; det.? 1; complete? 1
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F(Ga R (b | Ga))
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DRA: 10st.; BA: 10st.; det.? 0; complete? 0
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!c U (!c & !a)
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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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!c | FGb
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DRA: 4st.; BA: 5st.; det.? 0; complete? 0
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G(c U a)
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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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c & Gb
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DRA: 3st.; BA: 2st.; 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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#+end_example
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An important point you should be aware of when comparing these numbers
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@ -20,14 +20,15 @@ ltl2tgba -f 'Fa & GFb'
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#+RESULTS:
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#+begin_example
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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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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"]
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0 -> 0 [label="b\n{0}"]
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0 -> 0 [label="!b"]
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1 [label="1"]
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1 -> 1 [label="!a\n"]
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1 -> 2 [label="a\n"]
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2 [label="2"]
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2 -> 2 [label="b\n{Acc[b]}"]
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2 -> 2 [label="!b\n"]
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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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@ -54,14 +55,15 @@ ltl2tgba "Fa & GFb" | sed 's/\\/\\\\/'
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#+RESULTS: dotex
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#+begin_example
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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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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"]
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0 -> 0 [label="b\\n{0}"]
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0 -> 0 [label="!b"]
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1 [label="1"]
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1 -> 2 [label="a\\n"]
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1 -> 1 [label="!a\\n"]
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2 [label="2"]
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2 -> 2 [label="b\\n{Acc[b]}"]
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2 -> 2 [label="!b\\n"]
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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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@ -72,17 +74,17 @@ $txt
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#+RESULTS:
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[[file:dotex.png]]
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The string between braces, =Acc[b]=, represents an acceptance set (its
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actual name is not really important): any transition labeled by
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=Acc[b]= belongs to the =Acc[b]= acceptance set. You may have many
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transitions in the same acceptance set, and a transition may also
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belong to multiple acceptance sets. An infinite path through this
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automaton is accepting iff it visit each acceptance set infinitely
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often. Therefore, in the above example, any accepted path will
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/necessarily/ leave the initial state after a finite amount of steps,
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and then it will verify the property =b= infinitely often. It is also
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possible that an automaton do not use any acceptance set at all, in
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which any run is accepting.
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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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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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@ -91,30 +93,36 @@ Here is a TGBA with multiple acceptance sets (we omit the call to
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ltl2tgba 'GFa & GFb'
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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="1"]
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: 1 -> 1 [label="a & b\n{Acc[b], Acc[a]}"]
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: 1 -> 1 [label="b & !a\n{Acc[b]}"]
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: 1 -> 1 [label="a & !b\n{Acc[a]}"]
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: 1 -> 1 [label="!b & !a\n"]
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: }
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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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#+END_SRC
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#+RESULTS: dotex2
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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="1"]
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: 1 -> 1 [label="a & b\\n{Acc[b], Acc[a]}"]
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: 1 -> 1 [label="b & !a\\n{Acc[b]}"]
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: 1 -> 1 [label="a & !b\\n{Acc[a]}"]
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: 1 -> 1 [label="!b & !a\\n"]
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: }
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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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#+BEGIN_SRC dot :file dotex2.png :cmdline -Tpng :var txt=dotex2 :exports results
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$txt
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@ -122,9 +130,9 @@ $txt
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#+RESULTS:
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[[file:dotex2.png]]
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The above TGBA has two acceptance sets: =Acc[a]= and =Acc[b]=.
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The position of these acceptance sets ensures that =a= and =b= atomic
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proposition must be true infinitely often.
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The above TGBA has two acceptance sets: =0= and =1=. 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:
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@ -135,19 +143,20 @@ ltl2tgba -B 'GFa & GFb'
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#+RESULTS:
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#+begin_example
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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", peripheries=2]
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1 -> 1 [label="a & b\n{Acc[1]}"]
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1 -> 2 [label="b & !a\n{Acc[1]}"]
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1 -> 3 [label="!b\n{Acc[1]}"]
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2 [label="1"]
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2 -> 1 [label="a\n"]
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2 -> 2 [label="!a\n"]
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3 [label="2"]
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3 -> 1 [label="a & b\n"]
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3 -> 2 [label="b & !a\n"]
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3 -> 3 [label="!b\n"]
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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", peripheries=2]
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0 -> 0 [label="a & b"]
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0 -> 1 [label="!b"]
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0 -> 2 [label="!a & b"]
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1 [label="1"]
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1 -> 0 [label="a & b"]
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1 -> 1 [label="!b"]
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1 -> 2 [label="!a & b"]
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2 [label="2"]
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2 -> 0 [label="a"]
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2 -> 2 [label="!a"]
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}
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#+end_example
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@ -158,19 +167,20 @@ ltl2tgba -B 'GFa & GFb' | sed 's/\\/\\\\/'
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#+RESULTS: dotex2ba
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#+begin_example
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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", peripheries=2]
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1 -> 1 [label="a & b\\n{Acc[1]}"]
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1 -> 2 [label="b & !a\\n{Acc[1]}"]
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1 -> 3 [label="!b\\n{Acc[1]}"]
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2 [label="1"]
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2 -> 1 [label="a\\n"]
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2 -> 2 [label="!a\\n"]
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3 [label="2"]
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3 -> 1 [label="a & b\\n"]
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3 -> 2 [label="b & !a\\n"]
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3 -> 3 [label="!b\\n"]
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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
|
||||
|
||||
|
|
@ -182,25 +192,93 @@ $txt
|
|||
|
||||
Although accepting states in the Büchi automaton are pictured with
|
||||
double-lines, internally this automaton is still handled as a TGBA
|
||||
with a single acceptance set =Acc[1]= such that the transitions
|
||||
with a single acceptance set such that the transitions
|
||||
leaving the state are either all accepting, or all non-accepting.
|
||||
This is the reason why the =Acc[1]= sets are still shown in the
|
||||
output: it shows that a Büchi automaton is (a special case of) a TGBA.
|
||||
You can see this underlying TGBA if you pass the =--dot=t= option
|
||||
(the =t= requests the use of transition-based acceptance at it
|
||||
is done internally):
|
||||
|
||||
Various options controls the output format of =ltl2tgba=:
|
||||
#+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/\\/\\\\/'
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS: dotex2ba-t
|
||||
#+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
|
||||
|
||||
#+BEGIN_SRC dot :file dotex2ba-t.png :cmdline -Tpng :var txt=dotex2ba-t :exports results
|
||||
$txt
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
[[file:dotex2ba-t.png]]
|
||||
|
||||
As already discussed on the page about [[file:oaut.org][common output options]], various
|
||||
options controls the output format of =ltl2tgba=:
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports results
|
||||
ltl2tgba --help | sed -n '/Output format:/,/^$/p' | sed '1d;$d'
|
||||
#+END_SRC
|
||||
#+RESULTS:
|
||||
: -8, --utf8 enable UTF-8 characters in output (ignored with
|
||||
: --lbtt or --spin)
|
||||
: --dot GraphViz's format (default)
|
||||
: --lbtt LBTT's format
|
||||
: -s, --spin Spin neverclaim (implies --ba)
|
||||
: --spot SPOT's format
|
||||
: --stats=FORMAT output statistics about the automaton
|
||||
|
||||
#+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
|
||||
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
|
||||
--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
|
||||
-q, --quiet suppress all normal output
|
||||
-s, --spin Spin neverclaim (implies --ba)
|
||||
--spot SPOT's format
|
||||
--stats=FORMAT output statistics about the automaton
|
||||
#+end_example
|
||||
|
||||
Option =-8= can be used to improve the readability of the output
|
||||
if your system can display UTF-8 correctly.
|
||||
|
|
@ -211,19 +289,20 @@ ltl2tgba -B8 'GFa & GFb'
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0", peripheries=2]
|
||||
1 -> 1 [label="a∧b\n{Acc[1]}"]
|
||||
1 -> 2 [label="b∧a̅\n{Acc[1]}"]
|
||||
1 -> 3 [label="b̅\n{Acc[1]}"]
|
||||
2 [label="1"]
|
||||
2 -> 1 [label="a\n"]
|
||||
2 -> 2 [label="a̅\n"]
|
||||
3 [label="2"]
|
||||
3 -> 1 [label="a∧b\n"]
|
||||
3 -> 2 [label="b∧a̅\n"]
|
||||
3 -> 3 [label="b̅\n"]
|
||||
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
|
||||
|
||||
|
|
@ -234,19 +313,20 @@ ltl2tgba -B8 "GFa & GFb" | sed 's/\\/\\\\/'
|
|||
#+RESULTS: dotex2ba8
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="0", peripheries=2]
|
||||
1 -> 1 [label="a∧b\\n{Acc[1]}"]
|
||||
1 -> 2 [label="b∧a̅\\n{Acc[1]}"]
|
||||
1 -> 3 [label="b̅\\n{Acc[1]}"]
|
||||
2 [label="1"]
|
||||
2 -> 1 [label="a\\n"]
|
||||
2 -> 2 [label="a̅\\n"]
|
||||
3 [label="2"]
|
||||
3 -> 1 [label="a∧b\\n"]
|
||||
3 -> 2 [label="b∧a̅\\n"]
|
||||
3 -> 3 [label="b̅\\n"]
|
||||
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
|
||||
|
||||
|
|
@ -272,19 +352,19 @@ never { /* G(Fa & Fb) */
|
|||
accept_init:
|
||||
if
|
||||
:: ((a) && (b)) -> goto accept_init
|
||||
:: ((b) && (!((a)))) -> goto T0_S2
|
||||
:: ((!((b)))) -> goto T0_S3
|
||||
:: ((!(b))) -> goto T0_S2
|
||||
:: ((!(a)) && (b)) -> goto T0_S3
|
||||
fi;
|
||||
T0_S2:
|
||||
if
|
||||
:: ((a)) -> goto accept_init
|
||||
:: ((!((a)))) -> goto T0_S2
|
||||
:: ((a) && (b)) -> goto accept_init
|
||||
:: ((!(b))) -> goto T0_S2
|
||||
:: ((!(a)) && (b)) -> goto T0_S3
|
||||
fi;
|
||||
T0_S3:
|
||||
if
|
||||
:: ((a) && (b)) -> goto accept_init
|
||||
:: ((b) && (!((a)))) -> goto T0_S2
|
||||
:: ((!((b)))) -> goto T0_S3
|
||||
:: ((a)) -> goto accept_init
|
||||
:: ((!(a))) -> goto T0_S3
|
||||
fi;
|
||||
}
|
||||
#+end_example
|
||||
|
|
@ -348,18 +428,19 @@ ltl2tgba 'Ga|Gb|Gc'
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="1"]
|
||||
1 -> 2 [label="b\n"]
|
||||
1 -> 3 [label="c\n"]
|
||||
1 -> 4 [label="a\n"]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label="b\n"]
|
||||
3 [label="3"]
|
||||
3 -> 3 [label="c\n"]
|
||||
4 [label="4"]
|
||||
4 -> 4 [label="a\n"]
|
||||
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
|
||||
|
||||
|
|
@ -370,18 +451,19 @@ ltl2tgba "Ga|Gb|Gc" | sed 's/\\/\\\\/'
|
|||
#+RESULTS: gagbgc1
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="1"]
|
||||
1 -> 2 [label="c\\n"]
|
||||
1 -> 3 [label="b\\n"]
|
||||
1 -> 4 [label="a\\n"]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label="c\\n"]
|
||||
3 [label="3"]
|
||||
3 -> 3 [label="b\\n"]
|
||||
4 [label="4"]
|
||||
4 -> 4 [label="a\\n"]
|
||||
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
|
||||
|
||||
|
|
@ -397,34 +479,35 @@ ltl2tgba -D 'Ga|Gb|Gc'
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="6"]
|
||||
1 -> 1 [label="a & b & c\n{Acc[1]}"]
|
||||
1 -> 2 [label="b & c & !a\n{Acc[1]}"]
|
||||
1 -> 3 [label="a & c & !b\n{Acc[1]}"]
|
||||
1 -> 4 [label="c & !a & !b\n{Acc[1]}"]
|
||||
1 -> 5 [label="a & b & !c\n{Acc[1]}"]
|
||||
1 -> 6 [label="b & !a & !c\n{Acc[1]}"]
|
||||
1 -> 7 [label="a & !b & !c\n{Acc[1]}"]
|
||||
2 [label="2"]
|
||||
2 -> 2 [label="b & c\n{Acc[1]}"]
|
||||
2 -> 4 [label="c & !b\n{Acc[1]}"]
|
||||
2 -> 6 [label="b & !c\n{Acc[1]}"]
|
||||
3 [label="4"]
|
||||
3 -> 3 [label="a & c\n{Acc[1]}"]
|
||||
3 -> 4 [label="c & !a\n{Acc[1]}"]
|
||||
3 -> 7 [label="a & !c\n{Acc[1]}"]
|
||||
4 [label="1"]
|
||||
4 -> 4 [label="c\n{Acc[1]}"]
|
||||
5 [label="5"]
|
||||
5 -> 5 [label="a & b\n{Acc[1]}"]
|
||||
5 -> 6 [label="b & !a\n{Acc[1]}"]
|
||||
5 -> 7 [label="a & !b\n{Acc[1]}"]
|
||||
6 [label="3"]
|
||||
6 -> 6 [label="b\n{Acc[1]}"]
|
||||
7 [label="0"]
|
||||
7 -> 7 [label="a\n{Acc[1]}"]
|
||||
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
|
||||
|
||||
|
|
@ -435,34 +518,35 @@ ltl2tgba -D 'Ga|Gb|Gc' | sed 's/\\/\\\\/'
|
|||
#+RESULTS: gagbgc2
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="6"]
|
||||
1 -> 1 [label="a & b & c\\n{Acc[1]}"]
|
||||
1 -> 2 [label="b & c & !a\\n{Acc[1]}"]
|
||||
1 -> 3 [label="a & c & !b\\n{Acc[1]}"]
|
||||
1 -> 4 [label="c & !a & !b\\n{Acc[1]}"]
|
||||
1 -> 5 [label="a & b & !c\\n{Acc[1]}"]
|
||||
1 -> 6 [label="b & !a & !c\\n{Acc[1]}"]
|
||||
1 -> 7 [label="a & !b & !c\\n{Acc[1]}"]
|
||||
2 [label="1"]
|
||||
2 -> 2 [label="b & c\\n{Acc[1]}"]
|
||||
2 -> 4 [label="c & !b\\n{Acc[1]}"]
|
||||
2 -> 6 [label="b & !c\\n{Acc[1]}"]
|
||||
3 [label="2"]
|
||||
3 -> 3 [label="a & c\\n{Acc[1]}"]
|
||||
3 -> 4 [label="c & !a\\n{Acc[1]}"]
|
||||
3 -> 7 [label="a & !c\\n{Acc[1]}"]
|
||||
4 [label="0"]
|
||||
4 -> 4 [label="c\\n{Acc[1]}"]
|
||||
5 [label="4"]
|
||||
5 -> 5 [label="a & b\\n{Acc[1]}"]
|
||||
5 -> 6 [label="b & !a\\n{Acc[1]}"]
|
||||
5 -> 7 [label="a & !b\\n{Acc[1]}"]
|
||||
6 [label="3"]
|
||||
6 -> 6 [label="b\\n{Acc[1]}"]
|
||||
7 [label="5"]
|
||||
7 -> 7 [label="a\\n{Acc[1]}"]
|
||||
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
|
||||
|
||||
|
|
@ -556,14 +640,18 @@ ltl2tgba --help | sed -n '/^ *%/p'
|
|||
%% a single %
|
||||
%a number of acceptance sets
|
||||
%c number of SCCs
|
||||
%d 1 if the automaton is deterministic, 0 otherwise
|
||||
%d 1 if the output is deterministic, 0 otherwise
|
||||
%e number of edges
|
||||
%f the formula, in Spot's syntax
|
||||
%n number of nondeterministic states
|
||||
%p 1 if the automaton is complete, 0 otherwise
|
||||
%r translation time (including pre- and
|
||||
%F name of the input file
|
||||
%L location in the input file
|
||||
%m name of the automaton
|
||||
%n number of nondeterministic states in output
|
||||
%p 1 if the output is complete, 0 otherwise
|
||||
%r processing time (excluding parsing) in seconds
|
||||
%s number of states
|
||||
%t number of transitions
|
||||
%w one word accepted by the output automaton
|
||||
#+end_example
|
||||
|
||||
For instance we can study the size of the automata generated for the
|
||||
|
|
@ -618,19 +706,21 @@ ltl2tgba -M '(Xa & Fb) | Gc'
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
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="1\n"]
|
||||
1 -> 3 [label="c\n"]
|
||||
1 -> 2 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 4 [label="a\n"]
|
||||
2 -> 2 [label="1"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 3 [label="c\n"]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 4 [label="1\n"]
|
||||
3 -> 3 [label="c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
#+NAME: monitor1
|
||||
#+BEGIN_SRC sh :results verbatim :exports none
|
||||
ltl2tgba -M '(Xa & Fb) | Gc' | sed 's/\\/\\\\/'
|
||||
|
|
@ -639,17 +729,18 @@ ltl2tgba -M '(Xa & Fb) | Gc' | sed 's/\\/\\\\/'
|
|||
#+RESULTS: monitor1
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
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="1\\n"]
|
||||
1 -> 3 [label="c\\n"]
|
||||
1 -> 2 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 4 [label="a\\n"]
|
||||
2 -> 2 [label="1"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 3 [label="c\\n"]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 4 [label="1\\n"]
|
||||
3 -> 3 [label="c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -666,20 +757,21 @@ ltl2tgba -MD '(Xa & Fb) | Gc'
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
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 -> 2 [label="c\n"]
|
||||
1 -> 3 [label="!c\n"]
|
||||
2 [label="4", peripheries=2]
|
||||
2 -> 4 [label="a\n"]
|
||||
2 -> 5 [label="c & !a\n"]
|
||||
1 -> 0 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="c"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 4 [label="a\n"]
|
||||
4 [label="2", peripheries=2]
|
||||
4 -> 4 [label="1\n"]
|
||||
5 [label="0", peripheries=2]
|
||||
5 -> 5 [label="c\n"]
|
||||
3 -> 1 [label="!c"]
|
||||
3 -> 4 [label="c"]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 0 [label="a"]
|
||||
4 -> 2 [label="!a & c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -691,20 +783,21 @@ ltl2tgba -MD '(Xa & Fb) | Gc' | sed 's/\\/\\\\/'
|
|||
#+RESULTS: monitor2
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
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 -> 2 [label="c\\n"]
|
||||
1 -> 3 [label="!c\\n"]
|
||||
2 [label="4", peripheries=2]
|
||||
2 -> 4 [label="a\\n"]
|
||||
2 -> 5 [label="c & !a\\n"]
|
||||
1 -> 0 [label="a"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 2 [label="c"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 4 [label="a\\n"]
|
||||
4 [label="2", peripheries=2]
|
||||
4 -> 4 [label="1\\n"]
|
||||
5 [label="0", peripheries=2]
|
||||
5 -> 5 [label="c\\n"]
|
||||
3 -> 1 [label="!c"]
|
||||
3 -> 4 [label="c"]
|
||||
4 [label="4", peripheries=2]
|
||||
4 -> 0 [label="a"]
|
||||
4 -> 2 [label="!a & c"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
|
|||
|
|
@ -23,22 +23,22 @@ ltl2tgta --ta --multiple-init 'a U Gb'
|
|||
#+begin_example
|
||||
digraph G {
|
||||
-1 [label="", style=invis, height=0]
|
||||
-1 -> 1 [label="a & b"]
|
||||
-1 -> 1 [label="!a & b"]
|
||||
-2 [label="", style=invis, height=0]
|
||||
-2 -> 2 [label="a & !b"]
|
||||
-2 -> 2 [label="a & b"]
|
||||
-3 [label="", style=invis, height=0]
|
||||
-3 -> 3 [label="b & !a"]
|
||||
1 [label="0\na & b",shape=box]
|
||||
1 -> 3 [label="{a}\n"]
|
||||
1 -> 2 [label="{b}\n"]
|
||||
-3 -> 3 [label="a & !b"]
|
||||
1 [label="2\n!a & b",shape=box]
|
||||
1 -> 4 [label="{a}\n"]
|
||||
2 [label="1\na & !b"]
|
||||
2 -> 1 [label="{b}\n"]
|
||||
2 -> 3 [label="{a, b}\n"]
|
||||
3 [label="2\nb & !a",shape=box]
|
||||
3 -> 4 [label="{a}\n"]
|
||||
2 [label="1\na & b",shape=box]
|
||||
2 -> 4 [label="{a}\n"]
|
||||
2 -> 1 [label="{a}\n"]
|
||||
2 -> 3 [label="{b}\n"]
|
||||
3 [label="0\na & !b"]
|
||||
3 -> 2 [label="{b}\n"]
|
||||
3 -> 1 [label="{a, b}\n"]
|
||||
4 [label="3",peripheries=2,shape=box]
|
||||
4 -> 4 [label="{a}\n{Acc[1]}"]
|
||||
4 -> 4 [label="{a}\n{0}"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -50,22 +50,22 @@ ltl2tgta --ta --multiple-init 'a U Gb' | sed 's/\\/\\\\/'
|
|||
#+begin_example
|
||||
digraph G {
|
||||
-1 [label="", style=invis, height=0]
|
||||
-1 -> 1 [label="a & !b"]
|
||||
-1 -> 1 [label="!a & b"]
|
||||
-2 [label="", style=invis, height=0]
|
||||
-2 -> 2 [label="b & !a"]
|
||||
-2 -> 2 [label="a & b"]
|
||||
-3 [label="", style=invis, height=0]
|
||||
-3 -> 3 [label="a & b"]
|
||||
1 [label="2\\na & !b"]
|
||||
1 -> 3 [label="{b}\\n"]
|
||||
1 -> 2 [label="{a, b}\\n"]
|
||||
2 [label="0\\nb & !a",shape=box]
|
||||
-3 -> 3 [label="a & !b"]
|
||||
1 [label="2\\n!a & b",shape=box]
|
||||
1 -> 4 [label="{a}\\n"]
|
||||
2 [label="1\\na & b",shape=box]
|
||||
2 -> 4 [label="{a}\\n"]
|
||||
3 [label="1\\na & b",shape=box]
|
||||
3 -> 2 [label="{a}\\n"]
|
||||
3 -> 1 [label="{b}\\n"]
|
||||
3 -> 4 [label="{a}\\n"]
|
||||
2 -> 1 [label="{a}\\n"]
|
||||
2 -> 3 [label="{b}\\n"]
|
||||
3 [label="0\\na & !b"]
|
||||
3 -> 2 [label="{b}\\n"]
|
||||
3 -> 1 [label="{a, b}\\n"]
|
||||
4 [label="3",peripheries=2,shape=box]
|
||||
4 -> 4 [label="{a}\\n{Acc[1]}"]
|
||||
4 -> 4 [label="{a}\\n{0}"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -104,7 +104,7 @@ digraph G {
|
|||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label=init]
|
||||
1 -> 2 [label="b & !a\n"]
|
||||
1 -> 2 [label="!a & b\n"]
|
||||
1 -> 3 [label="a & b\n"]
|
||||
1 -> 4 [label="a & !b\n"]
|
||||
2 [label="2",shape=box]
|
||||
|
|
@ -117,7 +117,7 @@ digraph G {
|
|||
4 -> 3 [label="{b}\n"]
|
||||
4 -> 2 [label="{a, b}\n"]
|
||||
5 [label="4",peripheries=2,shape=box]
|
||||
5 -> 5 [label="{a}\n{Acc[1]}"]
|
||||
5 -> 5 [label="{a}\n{0}"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -131,20 +131,20 @@ digraph G {
|
|||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label=init]
|
||||
1 -> 2 [label="b & !a\\n"]
|
||||
1 -> 2 [label="!a & b\\n"]
|
||||
1 -> 3 [label="a & b\\n"]
|
||||
1 -> 4 [label="a & !b\\n"]
|
||||
2 [label="2",shape=box]
|
||||
2 -> 5 [label="{a}\\n"]
|
||||
3 [label="3",shape=box]
|
||||
3 -> 5 [label="{a}\\n"]
|
||||
3 -> 2 [label="{a}\\n"]
|
||||
3 -> 4 [label="{b}\\n"]
|
||||
3 -> 5 [label="{a}\\n"]
|
||||
4 [label="1"]
|
||||
4 -> 3 [label="{b}\\n"]
|
||||
4 -> 2 [label="{a, b}\\n"]
|
||||
5 [label="4",peripheries=2,shape=box]
|
||||
5 -> 5 [label="{a}\\n{Acc[1]}"]
|
||||
5 -> 5 [label="{a}\\n{0}"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -157,7 +157,7 @@ $txt
|
|||
The =--gba= option can be used to request a Generalized Testing
|
||||
Automaton, i.e., a Testing Automaton with Generalized Büchi
|
||||
acceptance. In that case double-enclosures are not used anymore, and
|
||||
Büchi accepting transitions are marked with the same ={Acc[x],Acc[y]}=
|
||||
Büchi accepting transitions are marked with the same ={0,1}=
|
||||
notation used in TGBA.
|
||||
|
||||
#+BEGIN_SRC sh :results verbatim :exports code
|
||||
|
|
@ -170,22 +170,22 @@ digraph G {
|
|||
0 -> 1
|
||||
1 [label=init]
|
||||
1 -> 2 [label="a & b\n"]
|
||||
1 -> 3 [label="b & !a\n"]
|
||||
1 -> 3 [label="!a & b\n"]
|
||||
1 -> 4 [label="a & !b\n"]
|
||||
1 -> 5 [label="!b & !a\n"]
|
||||
1 -> 5 [label="!a & !b\n"]
|
||||
2 [label="1",shape=box]
|
||||
2 -> 3 [label="{a}\n{Acc[b], Acc[a]}"]
|
||||
2 -> 4 [label="{b}\n{Acc[b], Acc[a]}"]
|
||||
2 -> 5 [label="{a, b}\n{Acc[b], Acc[a]}"]
|
||||
3 [label="4"]
|
||||
3 -> 2 [label="{a}\n{Acc[b]}"]
|
||||
3 -> 4 [label="{a, b}\n{Acc[b]}"]
|
||||
3 -> 5 [label="{b}\n{Acc[b]}"]
|
||||
2 -> 3 [label="{a}\n{0,1}"]
|
||||
2 -> 4 [label="{b}\n{0,1}"]
|
||||
2 -> 5 [label="{a, b}\n{0,1}"]
|
||||
3 [label="3"]
|
||||
3 -> 2 [label="{a}\n{1}"]
|
||||
3 -> 4 [label="{a, b}\n{1}"]
|
||||
3 -> 5 [label="{b}\n{1}"]
|
||||
4 [label="2"]
|
||||
4 -> 2 [label="{b}\n{Acc[a]}"]
|
||||
4 -> 3 [label="{a, b}\n{Acc[a]}"]
|
||||
4 -> 5 [label="{a}\n{Acc[a]}"]
|
||||
5 [label="3"]
|
||||
4 -> 2 [label="{b}\n{0}"]
|
||||
4 -> 3 [label="{a, b}\n{0}"]
|
||||
4 -> 5 [label="{a}\n{0}"]
|
||||
5 [label="4"]
|
||||
5 -> 2 [label="{a, b}\n"]
|
||||
5 -> 3 [label="{b}\n"]
|
||||
5 -> 4 [label="{a}\n"]
|
||||
|
|
@ -203,22 +203,22 @@ digraph G {
|
|||
0 -> 1
|
||||
1 [label=init]
|
||||
1 -> 2 [label="a & b\\n"]
|
||||
1 -> 3 [label="b & !a\\n"]
|
||||
1 -> 3 [label="!a & b\\n"]
|
||||
1 -> 4 [label="a & !b\\n"]
|
||||
1 -> 5 [label="!b & !a\\n"]
|
||||
1 -> 5 [label="!a & !b\\n"]
|
||||
2 [label="1",shape=box]
|
||||
2 -> 3 [label="{a}\\n{Acc[b], Acc[a]}"]
|
||||
2 -> 4 [label="{b}\\n{Acc[b], Acc[a]}"]
|
||||
2 -> 5 [label="{a, b}\\n{Acc[b], Acc[a]}"]
|
||||
3 [label="4"]
|
||||
3 -> 2 [label="{a}\\n{Acc[b]}"]
|
||||
3 -> 4 [label="{a, b}\\n{Acc[b]}"]
|
||||
3 -> 5 [label="{b}\\n{Acc[b]}"]
|
||||
2 -> 3 [label="{a}\\n{0,1}"]
|
||||
2 -> 4 [label="{b}\\n{0,1}"]
|
||||
2 -> 5 [label="{a, b}\\n{0,1}"]
|
||||
3 [label="3"]
|
||||
3 -> 2 [label="{a}\\n{1}"]
|
||||
3 -> 4 [label="{a, b}\\n{1}"]
|
||||
3 -> 5 [label="{b}\\n{1}"]
|
||||
4 [label="2"]
|
||||
4 -> 2 [label="{b}\\n{Acc[a]}"]
|
||||
4 -> 3 [label="{a, b}\\n{Acc[a]}"]
|
||||
4 -> 5 [label="{a}\\n{Acc[a]}"]
|
||||
5 [label="3"]
|
||||
4 -> 2 [label="{b}\\n{0}"]
|
||||
4 -> 3 [label="{a, b}\\n{0}"]
|
||||
4 -> 5 [label="{a}\\n{0}"]
|
||||
5 [label="4"]
|
||||
5 -> 2 [label="{a, b}\\n"]
|
||||
5 -> 3 [label="{b}\\n"]
|
||||
5 -> 4 [label="{a}\\n"]
|
||||
|
|
@ -233,7 +233,7 @@ $txt
|
|||
|
||||
The interpretation is similar to that of the TA. Execution that
|
||||
stutter in a livelock-accepting (square) state are accepting as well
|
||||
as execution that visit the =Acc[a]= and =Acc[b]= acceptance sets
|
||||
as execution that visit the =0= and =1= acceptance sets
|
||||
infinitely often. Those acceptance sets are carried by transitions,
|
||||
as in TGBAs.
|
||||
|
||||
|
|
@ -252,23 +252,23 @@ digraph G {
|
|||
0 -> 1
|
||||
1 [label=init]
|
||||
1 -> 2 [label="a & b\n"]
|
||||
1 -> 3 [label="b & !a\n"]
|
||||
1 -> 3 [label="!a & b\n"]
|
||||
1 -> 4 [label="a & !b\n"]
|
||||
1 -> 5 [label="!b & !a\n"]
|
||||
1 -> 5 [label="!a & !b\n"]
|
||||
2 [label="3"]
|
||||
2 -> 3 [label="{a}\n{Acc[b], Acc[a]}"]
|
||||
2 -> 4 [label="{b}\n{Acc[b], Acc[a]}"]
|
||||
2 -> 5 [label="{a, b}\n{Acc[b], Acc[a]}"]
|
||||
2 -> 2 [label="{}\n{Acc[b], Acc[a]}"]
|
||||
3 [label="4"]
|
||||
3 -> 2 [label="{a}\n{Acc[b]}"]
|
||||
3 -> 4 [label="{a, b}\n{Acc[b]}"]
|
||||
3 -> 5 [label="{b}\n{Acc[b]}"]
|
||||
2 -> 3 [label="{a}\n{0,1}"]
|
||||
2 -> 4 [label="{b}\n{0,1}"]
|
||||
2 -> 5 [label="{a, b}\n{0,1}"]
|
||||
2 -> 2 [label="{}\n{0,1}"]
|
||||
3 [label="2"]
|
||||
3 -> 2 [label="{a}\n{1}"]
|
||||
3 -> 4 [label="{a, b}\n{1}"]
|
||||
3 -> 5 [label="{b}\n{1}"]
|
||||
3 -> 3 [label="{}\n"]
|
||||
4 [label="2"]
|
||||
4 -> 2 [label="{b}\n{Acc[a]}"]
|
||||
4 -> 3 [label="{a, b}\n{Acc[a]}"]
|
||||
4 -> 5 [label="{a}\n{Acc[a]}"]
|
||||
4 [label="4"]
|
||||
4 -> 2 [label="{b}\n{0}"]
|
||||
4 -> 3 [label="{a, b}\n{0}"]
|
||||
4 -> 5 [label="{a}\n{0}"]
|
||||
4 -> 4 [label="{}\n"]
|
||||
5 [label="1"]
|
||||
5 -> 2 [label="{a, b}\n"]
|
||||
|
|
@ -289,25 +289,25 @@ digraph G {
|
|||
0 -> 1
|
||||
1 [label=init]
|
||||
1 -> 2 [label="a & b\\n"]
|
||||
1 -> 3 [label="b & !a\\n"]
|
||||
1 -> 3 [label="!a & b\\n"]
|
||||
1 -> 4 [label="a & !b\\n"]
|
||||
1 -> 5 [label="!b & !a\\n"]
|
||||
2 [label="1"]
|
||||
2 -> 3 [label="{a}\\n{Acc[b], Acc[a]}"]
|
||||
2 -> 4 [label="{b}\\n{Acc[b], Acc[a]}"]
|
||||
2 -> 5 [label="{a, b}\\n{Acc[b], Acc[a]}"]
|
||||
2 -> 2 [label="{}\\n{Acc[b], Acc[a]}"]
|
||||
3 [label="4"]
|
||||
3 -> 2 [label="{a}\\n{Acc[b]}"]
|
||||
3 -> 4 [label="{a, b}\\n{Acc[b]}"]
|
||||
3 -> 5 [label="{b}\\n{Acc[b]}"]
|
||||
1 -> 5 [label="!a & !b\\n"]
|
||||
2 [label="3"]
|
||||
2 -> 3 [label="{a}\\n{0,1}"]
|
||||
2 -> 4 [label="{b}\\n{0,1}"]
|
||||
2 -> 5 [label="{a, b}\\n{0,1}"]
|
||||
2 -> 2 [label="{}\\n{0,1}"]
|
||||
3 [label="2"]
|
||||
3 -> 2 [label="{a}\\n{1}"]
|
||||
3 -> 4 [label="{a, b}\\n{1}"]
|
||||
3 -> 5 [label="{b}\\n{1}"]
|
||||
3 -> 3 [label="{}\\n"]
|
||||
4 [label="3"]
|
||||
4 -> 2 [label="{b}\\n{Acc[a]}"]
|
||||
4 -> 3 [label="{a, b}\\n{Acc[a]}"]
|
||||
4 -> 5 [label="{a}\\n{Acc[a]}"]
|
||||
4 [label="4"]
|
||||
4 -> 2 [label="{b}\\n{0}"]
|
||||
4 -> 3 [label="{a, b}\\n{0}"]
|
||||
4 -> 5 [label="{a}\\n{0}"]
|
||||
4 -> 4 [label="{}\\n"]
|
||||
5 [label="2"]
|
||||
5 [label="1"]
|
||||
5 -> 2 [label="{a, b}\\n"]
|
||||
5 -> 3 [label="{b}\\n"]
|
||||
5 -> 4 [label="{a}\\n"]
|
||||
|
|
|
|||
|
|
@ -103,28 +103,27 @@ ltl2tgba -D -x sat-minimize "GF(a <-> XXb)"
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
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"]
|
||||
1 -> 2 [label="!b & !a\n"]
|
||||
1 -> 2 [label="b & !a\n{Acc[1]}"]
|
||||
1 -> 3 [label="a & b\n{Acc[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 -> 4 [label="!b & !a\n"]
|
||||
2 -> 4 [label="b & !a\n{Acc[1]}"]
|
||||
2 -> 3 [label="a & !b\n"]
|
||||
2 -> 3 [label="a & b\n{Acc[1]}"]
|
||||
3 [label="4"]
|
||||
3 -> 1 [label="a & !b\n{Acc[1]}"]
|
||||
3 -> 1 [label="a & b\n"]
|
||||
3 -> 2 [label="!b & !a\n{Acc[1]}"]
|
||||
3 -> 2 [label="b & !a\n"]
|
||||
4 [label="3"]
|
||||
4 -> 2 [label="!b & !a\n{Acc[1]}"]
|
||||
4 -> 4 [label="b & !a\n"]
|
||||
4 -> 3 [label="a & !b\n{Acc[1]}"]
|
||||
4 -> 3 [label="a & b\n"]
|
||||
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}"]
|
||||
}
|
||||
#+end_example
|
||||
|
||||
|
|
@ -135,28 +134,27 @@ ltl2tgba -D -x sat-minimize "GF(a <-> XXb)" | sed 's/\\/\\\\/'
|
|||
#+RESULTS: gfaexxb3
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
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"]
|
||||
1 -> 1 [label="a & b\\n{Acc[1]}"]
|
||||
1 -> 2 [label="!b & !a\\n"]
|
||||
1 -> 2 [label="b & !a\\n{Acc[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 -> 3 [label="!b & !a\\n"]
|
||||
2 -> 3 [label="b & !a\\n{Acc[1]}"]
|
||||
2 -> 4 [label="a & !b\\n"]
|
||||
2 -> 4 [label="a & b\\n{Acc[1]}"]
|
||||
2 -> 0 [label="a & !b"]
|
||||
2 -> 1 [label="b\\n{0}"]
|
||||
2 -> 3 [label="!a & !b"]
|
||||
3 [label="3"]
|
||||
3 -> 1 [label="a & !b\\n{Acc[1]}"]
|
||||
3 -> 3 [label="b & !a\\n"]
|
||||
3 -> 4 [label="!b & !a\\n{Acc[1]}"]
|
||||
3 -> 4 [label="a & b\\n"]
|
||||
4 [label="4"]
|
||||
4 -> 1 [label="a & !b\\n{Acc[1]}"]
|
||||
4 -> 1 [label="a & b\\n"]
|
||||
4 -> 2 [label="!b & !a\\n{Acc[1]}"]
|
||||
4 -> 2 [label="b & !a\\n"]
|
||||
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
|
||||
|
||||
|
|
@ -177,34 +175,36 @@ ltl2tgba -BD -x sat-minimize "GF(a <-> XXb)"
|
|||
#+RESULTS:
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 2 [label="!a\n{Acc[1]}"]
|
||||
1 -> 3 [label="a & !b\n{Acc[1]}"]
|
||||
1 -> 4 [label="a & b\n{Acc[1]}"]
|
||||
2 [label="2", peripheries=2]
|
||||
2 -> 1 [label="!b & !a\n{Acc[1]}"]
|
||||
2 -> 4 [label="a\n{Acc[1]}"]
|
||||
2 -> 5 [label="b & !a\n{Acc[1]}"]
|
||||
3 [label="4"]
|
||||
3 -> 1 [label="a & b\n"]
|
||||
3 -> 2 [label="b & !a\n"]
|
||||
3 -> 3 [label="a & !b\n"]
|
||||
3 -> 6 [label="!b & !a\n"]
|
||||
4 [label="3"]
|
||||
4 -> 1 [label="!b\n"]
|
||||
4 -> 3 [label="a & b\n"]
|
||||
4 -> 6 [label="b & !a\n"]
|
||||
5 [label="6"]
|
||||
5 -> 1 [label="!b\n"]
|
||||
5 -> 4 [label="a & b\n"]
|
||||
5 -> 5 [label="b & !a\n"]
|
||||
6 [label="5"]
|
||||
6 -> 1 [label="a & b\n"]
|
||||
6 -> 2 [label="b & !a\n"]
|
||||
6 -> 4 [label="a & !b\n"]
|
||||
6 -> 5 [label="!b & !a\n"]
|
||||
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
|
||||
|
||||
|
|
@ -215,35 +215,36 @@ ltl2tgba -BD -x sat-minimize "GF(a <-> XXb)" | sed 's/\\/\\\\/'
|
|||
#+RESULTS: gfaexxb4
|
||||
#+begin_example
|
||||
digraph G {
|
||||
0 [label="", style=invis, height=0]
|
||||
0 -> 1
|
||||
1 [label="1", peripheries=2]
|
||||
1 -> 1 [label="!b & !a\\n{Acc[1]}"]
|
||||
1 -> 2 [label="b & !a\\n{Acc[1]}"]
|
||||
1 -> 3 [label="a\\n{Acc[1]}"]
|
||||
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 -> 1 [label="!b & !a\\n"]
|
||||
2 -> 2 [label="b & !a\\n"]
|
||||
2 -> 3 [label="a & !b\\n"]
|
||||
2 -> 4 [label="a & b\\n"]
|
||||
3 [label="3", peripheries=2]
|
||||
3 -> 5 [label="!a\\n{Acc[1]}"]
|
||||
3 -> 6 [label="a\\n{Acc[1]}"]
|
||||
4 [label="5"]
|
||||
4 -> 1 [label="!b & !a\\n"]
|
||||
4 -> 5 [label="b & !a\\n"]
|
||||
4 -> 3 [label="a & !b\\n"]
|
||||
4 -> 6 [label="a & b\\n"]
|
||||
5 [label="4"]
|
||||
5 -> 1 [label="b & !a\\n"]
|
||||
5 -> 2 [label="!b & !a\\n"]
|
||||
5 -> 3 [label="a & b\\n"]
|
||||
5 -> 4 [label="a & !b\\n"]
|
||||
6 [label="6"]
|
||||
6 -> 1 [label="b & !a\\n"]
|
||||
6 -> 5 [label="!b & !a\\n"]
|
||||
6 -> 3 [label="a & b\\n"]
|
||||
6 -> 6 [label="a & !b\\n"]
|
||||
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
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue