General Algorithms for Testing the Ambiguity of Finite Automata

Allauzen, Cyril; Mohri, Mehryar; Rastogi, Ashish

General Algorithms for Testing the Ambiguity of Finite Automata

Authors

Allauzen, Cyril

Mohri, Mehryar

Rastogi, Ashish

Description

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $ε$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time $O(|A|_E^2)$, and finite or polynomial ambiguity in time $O(|A|_E^3)$. These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and are based on a general algorithm for the composition or intersection of automata. We also give an algorithm to determine the degree of polynomial ambiguity of a finite automaton $A$ that is polynomially ambiguous in time $O(|A|_E^3)$. Finally, we present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton.