System and method of epsilon removal of weighted automata and transducers
First Claim
1. A method of processing an automaton A, the method comprising:
- computing via a processor of ε
-closure C of an automaton as follows;
C[p]={(q,w);
q∈
ε
[p],d[p,q]=w∈
K−
{Ō
}}where ε
[p] represents a set of states reachable from “
p”
via a path labeled with ε
, d[p,g] represents an ε
-distance from p to q in the automaton A, K is a semiring, and w represents weights;
modifying outgoing transitions of each state “
p”
by;
removing each of the outgoing transitions labeled with an empty string; and
adding to each of the outgoing transitions leaving ones of the set of states “
p”
a non-empty-string transition, wherein each of the set of states “
q”
is left with its weights pre-{circle around (x)}-multiplied by an ε
-distance from a corresponding one of the set of states “
p”
to a respective one of the set of states “
q”
in the automaton A; and
applying the modified automaton A to process information in a field of at least one of;
speech recognition, speech synthesis and text processing.
0 Assignments
0 Petitions
Accused Products
Abstract
An improved ε-removal method is disclosed that computes for any input weighted automaton A with ε-transitions an equivalent weighted automaton B with no ε-transitions. The method comprises two main steps. The first step comprises computing for each state “p” of the automaton A its ε-closure. The second step in the method comprises modifying the outgoing transitions of each state “p” by removing those labeled with ε. The method next comprises adding to the set of transitions leaving the state “p” non-ε-transitions leaving each state “q” in the set of states reachable from “p” via a path labeled with ε with their weights pre-{circle around (x)}multiplied by the ε-distance from state “p” to state “q” in the automaton A. State “p” is a final state if some state “q” within the set of states reachable from “p” via a path labeled with ε is final and the final weight
37 Citations
10 Claims
-
1. A method of processing an automaton A, the method comprising:
-
computing via a processor of ε
-closure C of an automaton as follows;
C[p]={(q,w);
q∈
ε
[p],d[p,q]=w∈
K−
{Ō
}}where ε
[p] represents a set of states reachable from “
p”
via a path labeled with ε
, d[p,g] represents an ε
-distance from p to q in the automaton A, K is a semiring, and w represents weights;modifying outgoing transitions of each state “
p”
by;removing each of the outgoing transitions labeled with an empty string; and adding to each of the outgoing transitions leaving ones of the set of states “
p”
a non-empty-string transition, wherein each of the set of states “
q”
is left with its weights pre-{circle around (x)}-multiplied by an ε
-distance from a corresponding one of the set of states “
p”
to a respective one of the set of states “
q”
in the automaton A; andapplying the modified automaton A to process information in a field of at least one of;
speech recognition, speech synthesis and text processing. - View Dependent Claims (2, 3)
-
-
4. A method of processing an automaton A, the method comprising:
-
computing via a processor an ε
-closure for each state “
p”
of the automaton A;modifying outgoing transitions of each state “
p”
by;removing each of the outgoing transitions labeled with an empty string; and adding to each of the outgoing transitions leaving ones of the set of states “
p”
a non-empty-string transition, wherein each of the set of states “
q”
is left with its weights pre-{circle around (x)}-multiplied by an ε
-distance from a corresponding one of the set of states “
p”
to a respective one of the set of states “
q”
in the automaton A; andapplying the modified automaton A to process information in a field of at least one of;
speech recognition, speech synthesis and text processing. - View Dependent Claims (5, 6, 7)
-
-
8. A computer-readable medium storing instructions for controlling a computing device to process automaton A, the instructions comprising:
-
computing of ε
-closure C[p] of an automaton as follows;
C[p]={(q,w);
q∈
ε
[p],d[p,q]=w∈
K−
{Ō
}}where ε
[p] represents the set of states reachable from “
p”
via a path labeled with ε
, d[p,g] represents an ε
-distance from p to q in the automaton A, K is a semiring, and w represents weights;modifying outgoing transitions of each state “
p”
by;removing each of the outgoing transitions labeled with an empty string; and adding to each of the outgoing transitions leaving ones of the set of states “
p”
a non-empty-string transition, wherein each of the set of states “
q”
is left with its weights pre-{circle around (x)}-multiplied by an ε
-distance from a corresponding one of the set of states “
p”
to a respective one of the set of states “
q”
in the automaton A; andapplying the modified automaton A to process information in a field of at least one of;
speech recognition, speech synthesis and text processing. - View Dependent Claims (9, 10)
-
Specification