随机算法预期运行时间的最弱前提推理

Benjamin Lucien Kaminski, J. Katoen, C. Matheja, Federico Olmedo
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引用次数: 56

摘要

本文提出了一种wp- style的计算方法,用于获得随机化算法的期望运行时边界。它的应用包括确定随机算法的(可能是无限的)预期终止时间,并证明几乎是肯定的终止——程序是否在有限的预期时间内以概率1终止?我们提供了几个循环运行时边界的证明规则,并在一个简单的操作模型上证明了该方法的正确性。我们表明,我们的方法是一个保守的扩展尼尔森的方法的推理关于确定性程序的运行时间。我们分析了一些示例程序的期望运行时间,包括优惠券收集问题、一维随机漫步和随机二分搜索。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Weakest Precondition Reasoning for Expected Runtimes of Randomized Algorithms
This article presents a wp--style calculus for obtaining bounds on the expected runtime of randomized algorithms. Its application includes determining the (possibly infinite) expected termination time of a randomized algorithm and proving positive almost--sure termination—does a program terminate with probability one in finite expected time? We provide several proof rules for bounding the runtime of loops, and prove the soundness of the approach with respect to a simple operational model. We show that our approach is a conservative extension of Nielson’s approach for reasoning about the runtime of deterministic programs. We analyze the expected runtime of some example programs including the coupon collector’s problem, a one--dimensional random walk and a randomized binary search.
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