Weighted Branching Simulation Distance for Parametric Weighted Kripke Structures

TL;DR

This paper introduces a weighted branching simulation distance for parametric weighted Kripke structures, enabling approximate system comparisons and property verification through a computable, bounded-distance measure.

Contribution

It extends branching simulation to weighted, parametric systems with a new distance measure, allowing for approximate simulation and property analysis.

Findings

Distance provides a quantitative measure of system similarity.

Existence of an upper bound makes the distance computable.

Facilitates property verification in weighted CTL fragments.

Abstract

This paper concerns branching simulation for weighted Kripke structures with parametric weights. Concretely, we consider a weighted extension of branching simulation where a single transitions can be matched by a sequence of transitions while preserving the branching behavior. We relax this notion to allow for a small degree of deviation in the matching of weights, inducing a directed distance on states. The distance between two states can be used directly to relate properties of the states within a sub-fragment of weighted CTL. The problem of relating systems thus changes to minimizing the distance which, in the general parametric case, corresponds to finding suitable parameter valuations such that one system can approximately simulate another. Although the distance considers a potentially infinite set of transition sequences we demonstrate that there exists an upper bound on the length of relevant sequences, thereby establishing the computability of the distance.