In [1]:
import spot
spot.setup()

Let's build a small automaton to use as example.

In [2]:
aut = spot.translate('!a & G(Fa <-> XXb)'); aut
Out[2]:
Inf( ) [Büchi] 0 0 I->0 1 1 0->1 !a 2 2 1->2 a 3 3 1->3 !a 4 4 1->4 !a 2->2 a & b 2->3 !a & b 5 5 2->5 !a & b 3->2 a & b 3->3 !a & b 4->4 !a & !b 5->4 !a & b

Build an accepting run:

In [3]:
run = aut.accepting_run()
print(run)
Prefix:
  0
  |  !a
  1
  |  a
Cycle:
  2
  |  a & b	{0}

Accessing the contents of the run can be done via the prefix and cycle lists.

In [4]:
print(spot.bdd_format_formula(aut.get_dict(), run.prefix[0].label))
print(run.cycle[0].acc)
!a
{0}

To convert the run into a word, using spot.twa_word(). Note that our runs are labeled by Boolean formulas that are not necessarily a conjunction of all involved litterals. The word is just the projection of the run on its labels.

In [5]:
word = spot.twa_word(run)
print(word)           # print as a string
word                  # LaTeX-style representation in notebooks
!a; a; cycle{a & b}
Out[5]:
$\lnot a; a; \mathsf{cycle}\{a \land b\}$

A word can be represented as a collection of signals (one for each atomic proposition). The cycle part is shown twice.

In [6]:
word.show()
Out[6]:
abprefixcycle cycle

Accessing the different formulas (stored as BDDs) can be done again via the prefix and cycle lists.

In [7]:
print(spot.bdd_format_formula(aut.get_dict(), word.prefix[0]))
print(spot.bdd_format_formula(aut.get_dict(), word.prefix[1]))
print(spot.bdd_format_formula(aut.get_dict(), word.cycle[0]))
!a
a
a & b

Calling simplifify() will produce a shorter word that is compatible with the original word. For instance in the above word, the initial a is compatible with both a & b and a & !b. The word obtained by restricting a to a & b is therefore still accepted, allowing us to remove the prefix.

In [8]:
word.simplify()
print(word)
!a; cycle{a & b}

Such a simplified word can be created directly from the automaton:

In [9]:
aut.accepting_word()
Out[9]:
$\lnot a; \mathsf{cycle}\{a \land b\}$

Words can be created using the parse_word function:

In [10]:
print(spot.parse_word('a; b; cycle{a&b}'))
print(spot.parse_word('cycle{a&bb|bac&(aaa|bbb)}'))
print(spot.parse_word('a; b;b; qiwuei;"a;b&c;a" ;cycle{a}'))
a; b; cycle{a & b}
cycle{(a & bb) | (aaa & bac) | (bac & bbb)}
a; b; b; qiwuei; "a;b&c;a"; cycle{a}
In [11]:
# make sure that we can parse a word back after it has been printed
w = spot.parse_word(str(spot.parse_word('a;b&a;cycle{!a&!b;!a&b}'))); w
Out[11]:
$a; a \land b; \mathsf{cycle}\{\lnot a \land \lnot b; \lnot a \land b\}$
In [12]:
w.show()
Out[12]:
abprefixcycle cycle

Words can be easily converted to automata

In [13]:
w.as_automaton()
Out[13]:
t [all] 0 0 I->0 1 1 0->1 a 2 2 1->2 a & b 3 3 2->3 !a & !b 3->2 !a & b