`expression`.`is_equivalent`(`exp`)

Whether this expression is equivalent to exp, i.e., whether they accept the same words with the same weights.

Preconditions:

Both labelsets are free, or nullable of free
Both weightsets are either $\mathbb{B}, \mathbb{Z}$, or a field ($\mathbb{F}_2, \mathbb{Q}, \mathbb{Q}_\text{mp}, \mathbb{R}$).

Algorithm:

Compute the derived-term automaton of both expressions, and check whether the automata are equivalent.

Examples



In [1]:

    
import vcsn









    



:0: FutureWarning: IPython widgets are experimental and may change in the future.



In [2]:

    
b = vcsn.context('lal_char, b')
r1 = b.expression('a')
r2 = b.expression('b')
r1.is_equivalent(r2)









    Out[2]:





False



In [3]:

    
r1 = b.expression('a')
r2 = b.expression('a+a')
r1.is_equivalent(r2)









    Out[3]:





True



In [4]:

    
z = vcsn.context('lal_char, z')
r1 = z.expression('<42>a')
r2 = z.expression('<51>a')
r1.is_equivalent(r2)









    Out[4]:





False



In [5]:

    
r1 = z.expression('<42>a+<9>a')
r2 = z.expression('<51>a')
r1.is_equivalent(r2)









    Out[5]:





True

Note that rational expressions of different, but compatible, contexts, can be equivalent.



In [6]:

    
q = vcsn.context('lal_char, q')
z.expression('[abc]*').is_equivalent(q.expression('[abc]*'))









    Out[6]:





True



In [7]:

    
z.expression('<42>[abc]*').is_equivalent(q.expression('<51>[abc]*'))









    Out[7]:





False