Distances for Weighted Transition Systems: Games and Properties

TL;DR

This paper introduces a unified framework for defining and analyzing distances between weighted transition systems using game-theoretic methods, generalizing many existing approaches and providing recursive characterizations.

Contribution

It develops a general, unifying framework for distances in weighted transition systems, connecting trace and state distances through game-based recursive definitions.

Findings

Framework generalizes many existing system distances

Branching distances can be characterized recursively

Game-theoretic approach enables analysis of quantitative properties

Abstract

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a linear and a branching distance on states of such a transition system. We show that our framework generalizes and unifies a large variety of previously considered system distances, and we develop some general properties of our distances. We also show that if the trace distance admits a recursive characterization, then the corresponding branching distance can be obtained as a least fixed point to a similar recursive characterization. The central tool in our work is a theory of infinite path-building games with quantitative objectives.