automaton.complement.ipynb

Kernel: Python 3

automaton.complement

Produce an automaton that accepts the complement of the language of the input automaton.

Precondition:

• the labelset is free

• the weightset is $\mathbb{B}$

• the automaton is complete

• the automaton is deterministic

Postcondition:

• Result.is_complete()

• Result.is_deterministic()

See also:

• expression.complement

Examples

import vcsn
b = vcsn.context('lal_char(abc), b')

a = b.expression('a+b').standard().determinize().complete()
a

The prefix operator ~ invokes complement().

~a

c = a.complement()
c

a.shortest(2)

$\mathit{a} \oplus \mathit{b}$

c.shortest(10)

$\varepsilon \oplus \mathit{c} \oplus \mathit{aa} \oplus \mathit{ab} \oplus \mathit{ac} \oplus \mathit{ba} \oplus \mathit{bb} \oplus \mathit{bc} \oplus \mathit{ca} \oplus \mathit{cb}$