Efficient Coalgebraic Partition Refinement

TL;DR

This paper introduces a generic coalgebraic partition refinement algorithm that efficiently computes behavioural equivalence across various system types, matching or surpassing existing algorithms in performance.

Contribution

The paper presents a novel, generic algorithm for coalgebraic systems that achieves optimal runtime for multiple system classes, unifying and improving upon prior methods.

Findings

Runs in O(m log n) time for finite coalgebras

Matches best known algorithms for transition systems and automata

Improves algorithms for Segala systems

Abstract

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in reactive verification; coalgebraic generality implies in particular that we cover not only classical relational systems but also various forms of weighted systems. Under assumptions on the type functor that allow representing its finite coalgebras in terms of nodes and edges, our algorithm runs in time $\mathcal{O}(m\cdot \log n)$ where $n$ and $m$ are the numbers of nodes and edges, respectively. Instances of our generic algorithm thus match the runtime of the best known algorithms for unlabelled transition systems, Markov chains, and deterministic automata (with fixed alphabets), and improve the best known algorithms for Segala systems.