`automaton``.compose`

The (accessible part of the) composition of two transducers ($A_1$ and $A_2$).

Preconditions:

$A_1$ and $A_2$ are transducers
$A_1$ has at least 2 tapes
The second tape of $A_1$ must have the same labelset as the first tape of $A_2$

Postconditions:

$\forall u \in alphabet(A_1)^*, \; A_2.eval(A_1.eval(u)) = A_1.compose(A_2).eval(u)$

Examples



In [5]:

    
import vcsn
ctx1 = vcsn.context("lat<lal<char(ab)>, lal<char(jk)>>, b")
ctx2 = vcsn.context("lat<lal<char(jk)>, lal<char(xy)>>, b")



In [6]:

    
a1 = ctx1.expression("(a|k)(a|j) + (b|k)*").automaton()
a1









    Out[6]:



In [7]:

    
a2 = ctx2.expression("(k|y)(k|x)*").automaton()
a2









    Out[7]:

The result of the composition has a useless state. Note that only the accessible part has been computed.



In [8]:

    
a1.compose(a2)









    Out[8]:

Translations

The composition of a "translator" from French to English with one from English to Spanish is analogous to the computation of the French to Spanish "translator".



In [9]:

    
%%file fr2en
chien|dot
chat|cat









    



Overwriting fr2en



In [10]:

    
ctx = vcsn.context("lat<lan<char>, lan<char>>, b")
fr_to_en = ctx.trie('fr2en')
fr_to_en









    Out[10]:



In [11]:

    
en_to_es = ctx.expression("dog|perro + cat|gato").automaton()
en_to_es









    Out[11]:



In [12]:

    
fr_to_es = fr_to_en.compose(en_to_es)
fr_to_es









    Out[12]:

Relying on "string-letters"

This example follows the same path, but using letters that are strings.



In [13]:

    
import vcsn
ctx = vcsn.context("lat<lan<string>, lan<string>>, b")
ctx









    Out[13]:





$(\{\ldots\})^? \times (\{\ldots\})^?\rightarrow\mathbb{B}$



In [14]:

    
%%file fr2en
'chien'|'dog'
'chat'|'cat'
'oiseau'|'bird'
'souris'|'mouse'
'souris'|'mice'









    



Overwriting fr2en



In [15]:

    
fr2en = ctx.trie('fr2en')
fr2en









    Out[15]:



In [16]:

    
%%file en2es
'dog'|'perro'
'cat'|'gato'
'mouse'|'ratón'
'mice'|'ratones'









    



Overwriting en2es



In [17]:

    
en2es = ctx.trie('en2es')
en2es









    Out[17]:



In [18]:

    
fr2en.compose(en2es)









    Out[18]:

automaton.compose

Examples

Translations

Relying on "string-letters"

`automaton``.compose`