Proving almost-sure termination by omega-regular decomposition

Jianhui Chen, Fei He
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引用次数: 9

Abstract

Almost-sure termination is the most basic liveness property of probabilistic programs. We present a novel decomposition-based approach for proving almost-sure termination of probabilistic programs with complex control-flow structure and non-determinism. Our approach automatically decomposes the runs of the probabilistic program into a finite union of ω-regular subsets and then proves almost-sure termination of each subset based on the notion of localized ranking supermartingales. Compared to the lexicographic methods and the compositional methods, our approach does not require a lexicographic order over the ranking supermartingales as well as the so-called unaffecting condition. Thus it has high generality. We present the algorithm of our approach and prove its soundness, as well as its relative completeness. We show that our approach can be applied to some hard cases and the evaluation on the benchmarks of previous works shows the significant efficiency of our approach.
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通过正则分解证明几乎肯定终止
几乎确定终止是概率程序最基本的活动性质。本文提出了一种新的基于分解的方法来证明具有复杂控制流结构和非确定性的概率规划的几乎确定终止。我们的方法自动将概率程序的运行分解为ω-正则子集的有限并,然后基于局部排序上鞅的概念证明每个子集的几乎确定终止。与词典编纂方法和组合方法相比,我们的方法不需要词典编纂的顺序,也不需要所谓的不影响条件。因此具有较高的通用性。给出了该方法的算法,并证明了其正确性和相对完备性。我们证明了我们的方法可以应用于一些困难的情况,并且对以前工作的基准的评估表明了我们的方法的显着效率。
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