The quantitative linear-time–branching-time spectrum
Uli Fahrenberg, Axel Legay · Theoretical Computer Science · 2013
We present a distance-agnostic approach to quantitative verification. Taking as input an unspecified distance on system traces, or executions, we develop a game-based framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance. Thus we extend the classic linear-time–branching-time spectrum to a quantitative setting, parametrized by trace distance. We also prove a general transfer principle which allows us to transfer counterexamples from the qualitative to the quantitative setting, showing that all system distances are mutually topologically inequivalent.