# Minimal Separating Sequences for All Pairs of States

14 Mar 2016

Rick Smetsers, Joshua Moerman and David N. Jansen

## Abstract

Finding minimal separating sequences for all pairs of inequivalent states in a finite state machine is a classic problem in automata theory. Sets of minimal separating sequences, for instance, play a central role in many conformance testing methods. Moore has already outlined a partition refinement algorithm that constructs such a set of sequences in O(mn) time, where m is the number of transitions and n is the number of states. In this paper, we present an improved algorithm based on the minimization algorithm of Hopcroft that runs in O(m log n) time. The efficiency of our algorithm is empirically verified and compared to the traditional algorithm.