In [1]:
import vcsn
The synchronized product of Boolean automata computes the intersection of their languages. For instance, the conjunction of an automaton that accepts only words on $\{a, b\}$ with an odd number of $a$ with an automaton accepting with words with an odd number of $b$:
In [2]:
%%automaton odda
$ -> 0
0 -> 0 b
0 -> 1 a
1 -> 1 b
1 -> 0 a
1 -> $
In [3]:
%%automaton oddb
$ -> 0
0 -> 0 a
0 -> 1 b
1 -> 1 a
1 -> 0 b
1 -> $
is an automaton that accepts only words with odd numbers of $a$ and $b$:
In [4]:
odda & oddb
Out[4]:
In [5]:
(odda & oddb).shortest(10)
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In [6]:
import vcsn
c = vcsn.context('lal_char, seriesset<lal_char, z>')
std = lambda exp: c.expression(exp).standard()
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x = std("<x>a*+<x>b*"); x
Out[7]:
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y = std("<y>a*+<y>c*"); y
Out[8]:
In [9]:
x & y
Out[9]:
In [10]:
x = std('<x>a')
y = std('<y>a')
z = std('<z>a')
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x & y & z
Out[11]:
In [12]:
xy = (x & y).__value__(); xy & z
Out[12]:
The __value__ call here is an internal detail used to force Vcsn into the binary call. You should forget about it