`automaton`.`is_isomorphic`(`aut`)

Whether this automaton isomorphic to aut, i.e., whether they are "the same graph."

Preconditions:

Both automata are accessible

Examples

Boolean Automata

Automata are isomorphic if there is a bijection between their states.

The following function takes a (Boolean) rational expression, and return its standard automaton.



In [1]:

    
import vcsn

def aut(e):
    return vcsn.context('lal_char, b').expression(e, 'binary').standard()
a1 = aut('a*+b*'); a1









    Out[1]:



In [2]:

    
a2 = aut('b*+a*'); a2









    Out[2]:



In [3]:

    
a1.is_isomorphic(a2), a1 == a2









    Out[3]:





(True, False)

The automata must be accessible, but coaccessibility is not required.



In [4]:

    
%%automaton -s a1
$ -> 0
0 -> 1 a



In [5]:

    
%%automaton -s a2
$ -> 0
0 -> 1 b



In [6]:

    
a1.is_isomorphic(a1), a1.is_isomorphic(a2)









    Out[6]:





(True, False)

Equivalent automata can be non isomorphic.



In [7]:

    
a1 = aut('a+a')
a2 = aut('a')
a1.is_isomorphic(a2), a1.is_equivalent(a2)









    Out[7]:





(False, True)

Weighted Automata

We now build automaton weighted in $\mathbb{Q}$.



In [8]:

    
def aut(e):
    return vcsn.context('lal_char, z').expression(e, 'binary').standard()
a1 = aut('<2>a+<3>b')
a2 = aut('<3>b+<2>a')
a1.is_isomorphic(a2)









    Out[8]:





True



In [9]:

    
a1 = aut('<2>a')
a2 = aut('a+a')
a1.is_isomorphic(a2)









    Out[9]:





False

automaton.is_isomorphic(aut)

Examples

Boolean Automata

Weighted Automata

`automaton`.`is_isomorphic`(`aut`)