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]:

Build an accepting run:

In [3]:
run = aut.accepting_run()
print(run)

Prefix:
0
|  !a
1
|  !a
Cycle:
2
|  a & b	{0}
3
|  !a & b



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; !a & b}

Out[5]:
$\lnot a; \lnot a; \mathsf{cycle}\{a \land b; \lnot a \land b\}$

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]:

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]))
print(spot.bdd_format_formula(aut.get_dict(), word.cycle[1]))

!a
!a
a & b
!a & b


Calling simplify() will produce a shorter word that is compatible with the original word. For instance, in the above word the second a is compatible with !a & b, so the prefix can be shortened by rotating the cycle.

In [8]:
word.simplify()
print(word)

!a; cycle{!a & b; a & b}


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

In [9]:
aut.accepting_word()

Out[9]:
$\lnot a; \mathsf{cycle}\{\lnot a \land b; a \land b\}$

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]:

Words can be easily converted to automata

In [13]:
w.as_automaton()

Out[13]: