org: update hierarchy examples
* doc/org/hierarchy.org: Adjust for recent changes.
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Alexandre Duret-Lutz
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1 changed files with 34 additions and 41 deletions
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@ -314,23 +314,13 @@ $txt
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#+RESULTS:
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[[file:hier-oblig-1.svg]]
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Note that the above automaton uses transition-based acceptance, but
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since it is an obligation, using transition-based acceptance will not
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improve anything, so we might as well require a Büchi automaton with
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=-B= or just state-based acceptance with =-S=:
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#+NAME: hier-oblig-1b
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -B 'Fa R b' | autfilt --highlight-nondet -d
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#+END_SRC
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#+BEGIN_SRC dot :file hier-oblig-1b.svg :var txt=hier-oblig-1b :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:hier-oblig-1b.svg]]
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Note that the default translation used by =ltl2tgba= will turn any
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syntactic persistence formulas (this includes obligations formulas)
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into a weak automaton. In a weak automaton, the acceptance condition
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could be defined in term of SCCs, i.e., the cycles of some SCCs are
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either all accepting, or all rejecting. As a consequence, it there is
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no incentive to use transition-based acceptance; instead, state-based
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acceptance is output by default.
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With =ltl2tgba -D= we get a (minimal) deterministic weak Büchi
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automaton instead.
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@ -358,12 +348,13 @@ by =autfilt= when simplifying deterministic automata (they need to be
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deterministic so that =autfilt= can easily compute their complement).
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For instance, let us use =ltl2dstar= to construct a Streett automaton
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for the obligation property =a <-> GXa=:
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for the obligation property =Ga | XFb=.
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#+NAME: hier-oblig-3
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#+BEGIN_SRC sh :results verbatim :exports code
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ltldo 'ltl2dstar --automata=streett' -f 'a <-> GXa' -d
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ltldo 'ltl2dstar --automata=streett' -f 'Ga | XFb' -d
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#+END_SRC
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#+BEGIN_SRC dot :file hier-oblig-3.svg :var txt=hier-oblig-3 :exports results
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$txt
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#+END_SRC
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@ -375,7 +366,7 @@ We can now minimize this automaton with:
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#+NAME: hier-oblig-4
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#+BEGIN_SRC sh :results verbatim :exports code
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ltldo 'ltl2dstar --automata=streett' -f 'a <-> GXa' | autfilt -D -C -d
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ltldo 'ltl2dstar --automata=streett' -f 'Ga | XFb' | autfilt -D -C -d
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#+END_SRC
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#+BEGIN_SRC dot :file hier-oblig-4.svg :var txt=hier-oblig-4 :exports results
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$txt
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@ -597,12 +588,12 @@ a /recurrence/ property), is to chain a few algorithms implemented in Spot:
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1. Determinize the non-deterministic automaton to obtain a
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deterministic automaton with parity acceptance: this is done by
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using =ltl2tgba -G -D=, with option =-G= indicating that any
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acceptance condition may be used.
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using =ltl2tgba -P -D=, with option =-P= indicating that parity
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acceptance is desired.
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#+NAME: hier-recurrence-4
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -G -D 'G(Gb | Fa)' -d
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ltl2tgba -P -D 'G(Gb | Fa)' -d
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#+END_SRC
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#+BEGIN_SRC dot :file hier-recurrence-4.svg :var txt=hier-recurrence-4 :exports results
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$txt
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@ -617,7 +608,7 @@ a /recurrence/ property), is to chain a few algorithms implemented in Spot:
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#+NAME: hier-recurrence-5
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -G -D 'G(Gb | Fa)' |
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ltl2tgba -P -D 'G(Gb | Fa)' |
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autfilt --generalized-rabin -d
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#+END_SRC
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#+BEGIN_SRC dot :file hier-recurrence-5.svg :var txt=hier-recurrence-5 :exports results
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@ -636,7 +627,7 @@ a /recurrence/ property), is to chain a few algorithms implemented in Spot:
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#+NAME: hier-recurrence-6
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -G -D 'G(Gb | Fa)' |
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ltl2tgba -P -D 'G(Gb | Fa)' |
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autfilt -S --generalized-rabin -d
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#+END_SRC
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@ -659,7 +650,7 @@ a /recurrence/ property), is to chain a few algorithms implemented in Spot:
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#+NAME: hier-recurrence-7
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -G -D 'G(Gb | Fa)' |
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ltl2tgba -P -D 'G(Gb | Fa)' |
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autfilt -S --generalized-rabin |
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autfilt -B -D -d
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#+END_SRC
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@ -678,7 +669,7 @@ helps producing a smaller automaton. Here is what we get without it:
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#+NAME: hier-recurrence-8
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgba -G -D 'G(Gb | Fa)' |
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ltl2tgba -P -D 'G(Gb | Fa)' |
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autfilt --generalized-rabin |
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autfilt -B -D -d
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#+END_SRC
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@ -690,8 +681,9 @@ $txt
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#+RESULTS:
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[[file:hier-recurrence-8.svg]]
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It is likely that =ltl2tgba= will implement all this processing chain
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in the future.
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It is likely that =ltl2tgba -B -D= will implement all this processing
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chain in the future, but so originally =-D= was only expressing a
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preference not a requirement.
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** Persistence
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@ -735,13 +727,13 @@ Note that in this example, we know that =GFa= is trivial enough that
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general case we might have to determinize the automaton as we did in
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the previous section (we will do it again below).
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/Persistence/ properties can be represented by weak Büchi automata. The
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translator is aware of that, so when it detects that the input formula
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is a syntactic-persistence, it simplifies its translation slightly to
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ensure that the output will use at most one acceptance set. (It is
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possible to define a persistence properties using an LTL formula that
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is not a syntactic-persistance, this optimization is simply not
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applied.)
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/Persistence/ properties can be represented by weak Büchi automata.
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The translator is aware of that, so when it detects that the input
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formula is a syntactic-persistence, it simplifies its translation
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slightly to ensure that the output will use at most one acceptance
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set. (It is possible to define a persistence properties using an LTL
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formula that is not a syntactic-persistance, in that case this
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optimization is simply not applied.)
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If the input is a weak property that is not syntactically weak, the
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output will not necessarily be weak. One costly way to obtain a weak
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@ -751,7 +743,8 @@ complement the acceptance of the resulting automaton, yielding a
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deterministic co-Büchi automaton, and then transform that into a Büchi
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automaton.
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Let's do that on the persistence formula =F(G!a | G(b U a))=
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Let's do that on the persistence formula =F(G!a | G(b U a))=, just for
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the fun of it.
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#+BEGIN_SRC sh :results verbatim :exports both
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ltlfilt -f 'F(G!a | G(b U a))' --format='%[v]h'
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@ -772,7 +765,7 @@ $txt
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#+RESULTS:
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[[file:hier-persistence-3.svg]]
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Furthermore it appears that =ltl2tgba= does generate a deterministic
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Furthermore it appears that =ltl2tgba -D= does generate a deterministic
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Büchi automaton for the complement, instead we get a non-deterministic
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generalized Büchi automaton:
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@ -796,7 +789,7 @@ deterministic Büchi:
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#+NAME: hier-persistence-5
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#+BEGIN_SRC sh :results verbatim :exports code
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ltlfilt --negate -f 'F(G!a | G(b U a))' |
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ltl2tgba -G -D |
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ltl2tgba -P -D |
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autfilt --generalized-rabin |
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autfilt --tgba -D -d
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#+END_SRC
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@ -813,7 +806,7 @@ Now we can complement it to obtain a deterministic co-Büchi automaton for =F(G!
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#+NAME: hier-persistence-6
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#+BEGIN_SRC sh :results verbatim :exports code
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ltlfilt --negate -f 'F(G!a | G(b U a))' |
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ltl2tgba -G -D |
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ltl2tgba -P -D |
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autfilt --generalized-rabin |
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autfilt --tgba -D |
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autfilt --complement -d
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@ -831,7 +824,7 @@ And finally we convert the result back to Büchi:
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#+NAME: hier-persistence-7
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#+BEGIN_SRC sh :results verbatim :exports code
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ltlfilt --negate -f 'F(G!a | G(b U a))' |
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ltl2tgba -G -D |
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ltl2tgba -P -D |
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autfilt --generalized-rabin |
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autfilt --tgba -D |
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autfilt --complement -B -d
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