Proving Continuity of Coinductive Global Bisimulation Distances: A Never Ending Story

TL;DR

This paper introduces a novel global bisimulation distance based on transformation costs, extending to infinite processes, and discusses ongoing challenges in proving its continuity.

Contribution

It proposes a new coinductive bisimulation distance measure that extends existing notions to infinite processes and explores its fundamental properties.

Findings

Developed a global bisimulation distance based on process transformation costs.

Extended the distance to cover infinite but finitary trees using coinductive methods.

Obtained partial results on the continuity of the distance measure, with some open problems remaining.

Abstract

We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the cost of transformations: how much we need to modify one of the compared processes to obtain the other. Our original definition only covered finite processes, but a coinductive approach allows us to extend it to cover infinite but finitary trees. After having shown many interesting properties of our distance, it was our intention to prove continuity with respect to projections, but unfortunately the issue remains open. Nonetheless, we have obtained several partial results that are presented in this paper.