General Algorithms for Testing the Ambiguity of Finite Automata

TL;DR

This paper introduces efficient algorithms for testing the ambiguity levels of finite automata with epsilon-transitions, improving computational complexity and providing practical applications such as entropy approximation.

Contribution

It presents new algorithms with better complexity for testing finite, polynomial, and exponential ambiguity of automata, including a method to determine polynomial degree.

Findings

Algorithms for exponential ambiguity in O(|A|_E^2)

Algorithms for finite/polynomial ambiguity in O(|A|_E^3)

Application to approximate entropy computation of probabilistic automata

Abstract

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-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.