Automatic Equivalence Proofs for Non-deterministic Coalgebras

TL;DR

This paper introduces a new algorithm for deciding bisimilarity of generalized regular expressions for coalgebraic systems, implemented in CIRC, covering various system types like streams and automata.

Contribution

It presents a novel algorithm for automatic equivalence proofs of coalgebraic expressions, extending previous theoretical work with practical implementation.

Findings

Algorithm successfully decides bisimilarity for diverse systems

Implementation in CIRC demonstrates practical applicability

Validated on examples like streams, Mealy machines, and transition systems

Abstract

A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene's theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata, Mealy machines and labelled transition systems. In this paper, we present a novel algorithm to decide whether two expressions are bisimilar or not. The procedure is implemented in the automatic theorem prover CIRC, by reducing coinduction to an entailment relation between an algebraic specification and an appropriate set of equations. We illustrate the generality of the tool with three examples: infinite streams of real numbers, Mealy machines and labelled transition systems.