Abstract
AbstractWe tackle the problem of establishing the soundness of approximate bisimilarity with respect to PCTL and its relaxed semantics. To this purpose, we consider a notion of bisimilarity similar to the one introduced by Desharnais, Laviolette, and Tracol, which is parametric with respect to an approximation error \(\delta \), and to the depth \(n\) of the observation along traces. Essentially, our soundness theorem establishes that, when a state \(q\) satisfies a given formula up-to error \(\delta \) and steps \(n\), and \(q\) is bisimilar to \(q'\) up-to error \(\delta '\) and enough steps, we prove that \(q'\) also satisfies the formula up-to a suitable error \(\delta ''\) and steps \(n\). The new error \(\delta ''\) is computed from \(\delta ,\delta '\) and the formula, and only depends linearly on \(n\). We provide a detailed overview of our soundness proof.KeywordsPCTLProbabilistic processesApproximate bisimulation
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