automaton.is_cycle_ambiguous

Whether the automaton is cycle ambiguous, i.e., there exist a state $s$ and a label $x$ such that there is more than one cycle in $s$ labeled with $x$ .

Preconditions:

the labelset is free.

Examples

In [1]:

import vcsn

In [2]:

%%automaton -s a
context = "lal_char, b"
$ -> 0
0 -> $
0 -> 1 a
0 -> 2 a
1 -> 0 b
2 -> 0 b

At state $0$ , the automaton has two cycles "ab" so it is cycle ambiguous.

In [3]:

a.is_cycle_ambiguous()

True

In [4]:

%%automaton -s a
context = "lal_char, b"
$ -> 0
0 -> $
0 -> 1 a
0 -> 2 a
1 -> 0 b
2 -> 0 c

At state $0$ , the automaton has two cycles with different label "ab", "ac" so it is not cycle ambiguous (it is cycle-unambiguous).

In [5]:

a.is_cycle_ambiguous()

False

In [6]:

a = vcsn.context("lal_char(abc), b").ladybird(3)
a

Two cycles in $0$ with label "acac".

In [7]:

a.is_cycle_ambiguous()

True

In [8]:

%%automaton -s a
vcsn_context = "lal_char, b"
$ -> 0
0 -> $
0 -> 1 a
0 -> 2 a
1 -> 0 b
1 -> 3 b
2 -> 1 c
2 -> 2 b
3 -> 1 c

Two cycles in $0$ with label "babc".

In [9]:

a.is_cycle_ambiguous()

True

In [10]:

%%automaton -s a
$ -> 0
0 -> $
1 -> 2 a
1 -> 3 a
2 -> 1 b
3 -> 1 b

In [11]:

a.is_cycle_ambiguous()

True