org: fix sat-minimize example
Fixes #178. * doc/org/satmin.org: Use a different example, where tba-det does not work. Also adjust the text to automatically adjust to the size of the produced automata.
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Alexandre Duret-Lutz
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1 changed files with 33 additions and 25 deletions
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@ -73,7 +73,7 @@ deterministic automaton for =GF(a <-> XXb)=. Instead we get a 9-state
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non-deterministic automaton.
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#+BEGIN_SRC sh :results verbatim :exports both
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ltl2tgba -D "GF(a <-> XXb)" --stats='states=%s, det=%d'
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ltl2tgba -D 'GF(a <-> XXb)' --stats='states=%s, det=%d'
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#+END_SRC
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#+RESULTS:
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: states=9, det=0
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@ -88,7 +88,7 @@ On our example, =-x tba-det= successfully produces a deterministic
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TBA, but a non-minimal one:
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#+BEGIN_SRC sh :results verbatim :exports both
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ltl2tgba -D -x tba-det "GF(a <-> XXb)" --stats='states=%s, det=%d'
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ltl2tgba -D -x tba-det 'GF(a <-> XXb)' --stats='states=%s, det=%d'
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#+END_SRC
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#+RESULTS:
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: states=7, det=1
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@ -97,7 +97,7 @@ Option =-x sat-minimize= will turn-on SAT-based minimization. It also
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implies =-x tba-det=, so there is no need to supply both options.
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#+BEGIN_SRC sh :results verbatim :exports both
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ltl2tgba -D -x sat-minimize "GF(a <-> XXb)" --stats='states=%s, det=%d'
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ltl2tgba -D -x sat-minimize 'GF(a <-> XXb)' --stats='states=%s, det=%d'
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#+END_SRC
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#+RESULTS:
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: states=4, det=1
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@ -106,7 +106,7 @@ We can draw it:
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#+NAME: gfaexxb3
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -D -x sat-minimize "GF(a <-> XXb)" -d
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ltl2tgba -D -x sat-minimize 'GF(a <-> XXb)' -d
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#+END_SRC
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#+RESULTS: gfaexxb3
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#+begin_example
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@ -148,14 +148,14 @@ $txt
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#+RESULTS:
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[[file:gfaexxb3.png]]
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Clearly this is automaton benefits from the transition-based
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Clearly this automaton benefits from the transition-based
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acceptance. If we want a traditional Büchi automaton, with
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state-based acceptance, we only need to add the =-B= option. The
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result will of course be slightly bigger.
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#+NAME: gfaexxb4
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -BD -x sat-minimize "GF(a <-> XXb)" -d
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ltl2tgba -BD -x sat-minimize 'GF(a <-> XXb)' -d
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#+END_SRC
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#+RESULTS: gfaexxb4
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#+begin_example
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@ -207,10 +207,10 @@ There are cases where =ltl2tgba='s =tba-det= algorithm fails to produce a determ
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In that case, SAT-based minimization is simply skipped. For instance:
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#+BEGIN_SRC sh :results verbatim :exports both
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ltl2tgba -D -x sat-minimize "Ga R (F!b & (c U b))" --stats='states=%s, det=%d'
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ltl2tgba -D -x sat-minimize 'G(F(!b & (X!a M (F!a & F!b))) U !b)' --stats='states=%s, det=%d'
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#+END_SRC
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#+RESULTS:
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: states=5, det=1
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: states=5, det=0
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The question, of course, is whether there exist a deterministic
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automaton for this formula, in other words: is this a recurrence
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@ -224,10 +224,10 @@ without being syntactic recurrences.) [[file:ltlfilt.org][=ltlfilt=]] can be in
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print only formulas that are syntactic recurrences:
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#+BEGIN_SRC sh :results verbatim :exports both
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ltlfilt --syntactic-recurrence -f "Ga R (F!b & (c U b))"
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ltlfilt --syntactic-recurrence -f 'G(F(!b & (X!a M (F!a & F!b))) U !b)'
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#+END_SRC
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#+RESULTS:
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: Ga R (F!b & (c U b))
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: G(F(!b & (X!a M (F!a & F!b))) U !b)
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Since our input formula was output, it expresses a recurrence property.
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@ -237,35 +237,43 @@ output is guaranteed to be deterministic if and only if the input DRA
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expresses a recurrence property.
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#+BEGIN_SRC sh :results verbatim :exports both
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ltlfilt -f "Ga R (F!b & (c U b))" -l |
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ltlfilt --remove-wm -f 'G(F(!b & (X!a M (F!a & F!b))) U !b)' -l |
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ltl2dstar --ltl2nba=spin:ltl2tgba@-Ds - - |
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dstar2tgba -D --stats='input(states=%S) output(states=%s, acc-sets=%a, det=%d)'
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#+END_SRC
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#+RESULTS:
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: input(states=11) output(states=9, acc-sets=1, det=1)
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In the above command, =ltlfilt= is used to convert the LTL formula
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into =ltl2dstar='s syntax. Then =ltl2dstar= creates a deterministic
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Rabin automaton (using =ltl2tgba= as an LTL to BA translator), and the
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resulting 11-state DRA is converted into a 9-state DTBA by
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=dstar2tgba=. Since that result is deterministic, we can conclude
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that the formula was a recurrence.
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#+NAME: size
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#+BEGIN_SRC sh :exports none
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ltlfilt --remove-wm -f 'G(F(!b & (X!a M (F!a & F!b))) U !b)' -l |
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ltl2dstar --ltl2nba=spin:ltl2tgba@-Ds - - |
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dstar2tgba -D --stats=$arg
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#+END_SRC
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In the above command, =ltldo= is used to convert the LTL formula into
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=ltl2dstar='s syntax. Then =ltl2dstar= creates a deterministic Rabin
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automaton (using =ltl2tgba= as an LTL to BA translator), and the
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resulting call_size(arg="%S")[:results raw]-state DRA is converted
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into a call_size(arg="%s")[:results raw]-state DTBA by =dstar2tgba=.
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Since that result is deterministic, we can conclude that the formula
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was a recurrence.
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As far as SAT-based minimization goes, =dstar2tgba= will take the same
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options as =ltl2tgba=. For instance we can see that the smallest DTBA
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has 6 states:
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has call_size(arg="%s -x sat-minimize")[:results raw] states:
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#+BEGIN_SRC sh :results verbatim :exports both
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ltlfilt -f "Ga R (F!b & (c U b))" -l |
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ltlfilt --remove-wm -f 'G(F(!b & (X!a M (F!a & F!b))) U !b)' -l |
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ltl2dstar --ltl2nba=spin:ltl2tgba@-Ds - - |
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dstar2tgba -D -x sat-minimize --stats='input(states=%S) output(states=%s, acc-sets=%a, det=%d)'
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#+END_SRC
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#+RESULTS:
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: input(states=11) output(states=6, acc-sets=1, det=1)
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: input(states=11) output(states=4, acc-sets=1, det=1)
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* More acceptance sets
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The formula "=Ga R (F!b & (c U b))=" can in fact be minimized into an
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The formula "=G(F(!b & (X!a M (F!a & F!b))) U !b)=" can in fact be minimized into an
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even smaller automaton if we use multiple acceptance sets.
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Unfortunately because =dstar2tgba= does not know the formula being
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@ -276,12 +284,12 @@ number of acceptance sets can however be specified on the command-line
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with option =-x sat-acc=M=. For instance:
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#+BEGIN_SRC sh :results verbatim :exports both
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ltlfilt -f "Ga R (F!b & (c U b))" -l |
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ltlfilt --remove-wm -f 'G(F(!b & (X!a M (F!a & F!b))) U !b)' -l |
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ltl2dstar --ltl2nba=spin:ltl2tgba@-Ds - - |
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dstar2tgba -D -x sat-minimize,sat-acc=2 --stats='input(states=%S) output(states=%s, acc-sets=%a, det=%d)'
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#+END_SRC
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#+RESULTS:
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: input(states=11) output(states=5, acc-sets=2, det=1)
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: input(states=11) output(states=3, acc-sets=2, det=1)
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Beware that the size of the SAT problem is exponential in the number
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of acceptance sets (adding one acceptance set, in the input automaton
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@ -370,7 +378,7 @@ For our example, let us first generate a deterministic Rabin
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automaton with [[http://www.ltl2dstar.de/][=ltl2dstar=]].
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#+BEGIN_SRC sh :results silent :exports both
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ltlfilt -f "FGa | FGb" -l |
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ltlfilt -f 'FGa | FGb' -l |
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ltl2dstar --ltl2nba=spin:ltl2tgba@-Ds --output-format=hoa - - > output.hoa
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#+END_SRC
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@ -769,7 +777,7 @@ its iterations in this file.
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#+BEGIN_SRC sh :results verbatim :exports both
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rm -f stats.csv
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export SPOT_SATLOG=stats.csv
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ltlfilt -f "Ga R (F!b & (c U b))" -l |
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ltlfilt -f 'Ga R (F!b & (c U b))' -l |
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ltl2dstar --ltl2nba=spin:ltl2tgba@-Ds - - |
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dstar2tgba -D -x sat-minimize,sat-acc=2 --stats='input(states=%S) output(states=%s, acc-sets=%a, det=%d)'
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cat stats.csv
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