automaton.conjugate.ipynb

Kernel: Python 3

automaton.conjugate

Create the conjugate of an automaton. The conjugate of $\mathcal{A}$ is defined as the automaton recognizing the language $\{vu \mid u, v \in \Sigma^*\text{ and }uv\text{ recognized by }\mathcal{A}\}$.

Preconditions:

• labelset is nullable

Postconditions:

• None

Examples

import vcsn

ctx = vcsn.context('lan_char, b')
a = ctx.expression('ab*').automaton()
a

a.shortest(10)

$\mathit{a} \oplus \mathit{ab} \oplus \mathit{abb} \oplus \mathit{abbb} \oplus \mathit{abbbb} \oplus \mathit{abbbbb} \oplus \mathit{abbbbbb} \oplus \mathit{abbbbbbb} \oplus \mathit{abbbbbbbb} \oplus \mathit{abbbbbbbbb}$

conj = a.conjugate()
conj

conj.shortest(10)

$\mathit{a} \oplus \mathit{ab} \oplus \mathit{ba} \oplus \mathit{abb} \oplus \mathit{bab} \oplus \mathit{bba} \oplus \mathit{abbb} \oplus \mathit{babb} \oplus \mathit{bbab} \oplus \mathit{bbba}$