Distances for Weighted Transition Systems: Games and Properties

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrar y distance on system traces, we show how this leads to natural definitions of a linear and a branching d istance on states of such a transition system. We show that our framework generalizes and unifies a l arge 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 t he corresponding branching distance can be obtained as a least fixed point to a similar recursive charact erization. The central tool in our work is a theory of infinite path-building games with quantitative o bjectives.