概率PDL的Hennessy-Milner结果

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2020-10-01 DOI:10.1016/j.entcs.2020.09.014

Tao Gu, Alexandra Silva, Fabio Zanasi

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引用次数: 0

摘要

1985年，Kozen引入了概率命题动态逻辑(PPDL)，作为对概率程序进行推理的组合框架。本文研究了PPDL的可表达性，并给出了一系列类似于模态逻辑经典Hennessy-Milner定理的结果。首先，我们证明了PPDL表征了概率自动机(带输出)的概率轨迹等价。其次，我们证明PPDL可以适度扩展，以产生PPDL模型的概率状态双模拟的特征。第三，我们提供了PPDL的不同扩展，这次描述了概率事件双模拟。

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Hennessy-Milner Results for Probabilistic PDL

Kozen introduced probabilistic propositional dynamic logic (PPDL) in 1985 as a compositional framework to reason about probabilistic programs. In this paper we study expressiveness for PPDL and provide a series of results analogues to the classical Hennessy-Milner theorem for modal logic. First, we show that PPDL charaterises probabilistic trace equivalence of probabilistic automata (with outputs). Second, we show that PPDL can be mildly extended to yield a characterisation of probabilistic state bisimulation for PPDL models. Third, we provide a different extension of PPDL, this time characterising probabilistic event bisimulation.

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Electronic Notes in Theoretical Computer Science Computer Science-Computer Science (all)

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