Symbolic and Asynchronous Semantics via Normalized Coalgebras

TL;DR

This paper develops coalgebraic models for symbolic and asynchronous semantics of interactive systems, addressing the challenge of infinite behaviors and differing bisimilarity notions, with applications to open Petri nets and asynchronous pi-calculus.

Contribution

It introduces a coalgebraic framework for symbolic and asynchronous semantics, unifying their treatment and overcoming limitations of standard coalgebraic approaches.

Findings

Coalgebraic models for symbolic bisimilarity are proposed.

Application to asynchronous formalisms like Petri nets and pi-calculus.

Addresses infinite behaviors in interactive systems.

Abstract

The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons infinite, symbolic semantics were introduced as a mean to define smaller, possibly finite, transition systems, by employing symbolic actions and avoiding some sources of infiniteness. Unfortunately, symbolic bisimilarity has a different shape with respect to ordinary bisimilarity, and thus the standard coalgebraic characterization does not work. In this paper, we introduce its coalgebraic models. We will use as motivating examples two asynchronous formalisms: open Petri nets and asynchronous pi-calculus. Indeed, as we have shown in a previous paper, asynchronous bisimilarity can be seen as an instance of symbolic bisimilarity.