automaton.weight_series.ipynb

Kernel: Python 3

automaton.weight_series

Compute the sum of all the weights of the behavior. Find weighted distance between initial and final states.

Implementations:

• With a tropical weightset: Shortest path algorithm.

• Otherwise: Proper applied to the spontaneous version of the automaton, i.e., as if all the labels were replaced by the empty word.

Examples

import vcsn

In a Tropical Semiring

%%automaton a
context = "lal_char, zmin"
$ -> 0
0 -> 1 <6>a
0 -> 2 <1>a
2 -> 3 <1>b
3 -> 4 <1>c
4 -> 1 <1>d
0 -> 5 <2>a
5 -> 1 <3>b
1 -> $

a.weight_series()

$4$

In $\mathbb{Q}$

%%automaton b
context = "lal_char, q"
$ -> 0
0 -> 1 <6>a
0 -> 2 <1>a
2 -> 3 <1>b
3 -> 4 <1>c
4 -> 1 <1>d
0 -> 5 <2>a
5 -> 1 <3>b
1 -> $

b.weight_series()

$13$