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* doc/org/concepts.org (T-based vs. S-based acceptance): Adjust example.

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Alexandre Duret-Lutz 2022-09-09 16:41:44 +02:00
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doc/org/concepts.org
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@ -381,13 +381,14 @@ When /transition-based acceptance/ is used, acceptance sets are now
sets of /edges/ (or set of /transitions/ if you prefer), and runs are
accepting if the edges they visit satisfy the acceptance condition.
Here is an example of Transition-based Generalized Büchi Automaton
(TGBA).
Here is an example of Transition-based Büchi Automaton
(TBA).
#+NAME: tgba-example1
#+BEGIN_SRC sh
ltl2tgba 'GF(a & X(a U b))' -d
#+END_SRC
#+BEGIN_SRC dot :file concept-tgba1.svg :var txt=tgba-example1 :exports results
$txt
#+END_SRC
@ -399,27 +400,13 @@ This automaton accept all ω-words that infinitely often match the
pattern $a^+;b$ (that is: a positive number of letters where $a$ is
true are followed by one letter where $b$ is true).
Using transition-based acceptance allows for more compact automata.
The typical example is the LTL formula =GFa= (infinitely often $a$)
that can be represented using a one-state transition-based Büchi
automaton:
#+NAME: tgba-example2
#+BEGIN_SRC sh
ltl2tgba 'GFa' -d
#+END_SRC
#+BEGIN_SRC dot :file concept-tgba2.svg :var txt=tgba-example2 :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:concept-tgba2.svg]]
While the same property require a 2-state Büchi automaton using
Using transition-based acceptance often allows for more compact automata.
For instance the above automaton would need at least 3 states with
state-based acceptance:
#+NAME: tgba-example3
#+BEGIN_SRC sh
ltl2tgba 'GFa' -B -d
ltl2tgba 'GF(a & X(a U b))' -B -d
#+END_SRC
#+BEGIN_SRC dot :file concept-tba-vs-ba.svg :var txt=tgba-example3 :exports results
$txt