The Largest Respectful Function

TL;DR

This paper provides an explicit, constructive characterization of the largest respectful function, a key tool in simplifying bisimulation proofs in process algebra.

Contribution

It introduces a novel, explicit description of the largest respectful function, enhancing its practical applicability in bisimulation proofs.

Findings

Explicit characterization of the largest respectful function

Simplifies bisimulation proof techniques

Enhances understanding of respectful functions

Abstract

Respectful functions were introduced by Sangiorgi as a compositional tool to formulate short and clear bisimulation proofs. Usually, the larger the respectful function, the easier the bisimulation proof. In particular the largest respectful function, defined as the pointwise union of all respectful functions, has been shown to be very useful. We here provide an explicit and constructive characterization of it.