On the Average Complexity of Moore's State Minimization Algorithm

TL;DR

This paper proves that Moore's state minimization algorithm has an average complexity of O(n log n) for automata over any alphabet, with tight bounds for unary automata, advancing understanding of its efficiency.

Contribution

It establishes the average-case complexity of Moore's algorithm as O(n log n) for arbitrary automata, including tight bounds for unary cases.

Findings

Average complexity is O(n log n) for arbitrary automata.

Bound is tight for unary automata.

Results hold under uniform distribution over automata.

Abstract

We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with n states, the average complexity of Moore's state minimization algorithm is in O(n log n). Moreover this bound is tight in the case of unary utomata.