The quantitative linear-time–branching-time spectrum

Abstract : 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 provide fixed-point characterizations of all system distances, and we 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.
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Uli Fahrenberg, Axel Legay, Claus Thrane. The quantitative linear-time–branching-time spectrum. FSTTCS - IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Dec 2011, Mumbai, India. pp.54 - 69. ⟨hal-01088038⟩

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