Metrics for weighted transition systems: Axiomatization and complexity

Simulation distances are essentially an approximation of simulation which provide a measure of the extent by which behaviors in systems are inequivalent. In this paper, we consider the general quantitative model of weighted transition systems, where transitions are labeled with elements of a finite metric space. We study the so-called point-wise and accumulating simulation distances which provide extensions to the well-know Boolean notion of simulation on labeled transition systems. We introduce weighted process algebras for finite and regular behavior and offer sound and (approximate) complete inference systems for the proposed simulation distances. We also settle the algorithmic complexity of computing the simulation distances.