Bisimulations over DLTS in O(m.log n)-time

TL;DR

This paper introduces a new, simpler algorithm for computing the coarsest bisimulation over finite DLTS, achieving improved time complexity of O(m log n) without requiring the system to be complete.

Contribution

The paper presents a novel algorithm that computes the coarsest bisimulation over finite DLTS in O(m log n) time, improving upon existing methods and simplifying the process.

Findings

Algorithm runs in O(m log n) time

Does not require the DLTS to be complete

Uses O(k + m + n) space

Abstract

The well known Hopcroft's algorithm to minimize deterministic complete automata runs in $O(kn\log n)$-time, where $k$ is the size of the alphabet and $n$ the number of states. The main part of this algorithm corresponds to the computation of a coarsest bisimulation over a finite Deterministic Labelled Transition System (DLTS). By applying techniques we have developed in the case of simulations, we design a new algorithm which computes the coarsest bisimulation over a finite DLTS in $O(m\log n)$-time and $O(k+m+n)$-space, with $m$ the number of transitions. The underlying DLTS does not need to be complete and thus: $m\leq kn$. This new algorithm is much simpler than the two others found in the literature.