General Algorithms for Testing the Ambiguity of Finite Automata

Cyril Allauzen; Mehryar Mohri; Ashish Rastogi

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arXiv · 0802.3254

General Algorithms for Testing the Ambiguity of Finite Automata

Cyril Allauzen·Mehryar Mohri·Ashish Rastogi

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Abstract

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.

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BibTeX RIS

Cyril Allauzen, Mehryar Mohri, Ashish Rastogi. 2008-02-22. General Algorithms for Testing the Ambiguity of Finite Automata. https://arxiv.org/abs/0802.3254

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