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()

Examples



In [1]:

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



In [2]:

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









    Out[2]:

The prefix operator ~ invokes complement().



In [3]:

    
~a









    Out[3]:



In [4]:

    
c = a.complement()
c









    Out[4]:



In [5]:

    
a.shortest(2)









    Out[5]:





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



In [6]:

    
c.shortest(10)









    Out[6]:





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