论文标题

欧米茄规范性质的最佳修复

Optimal Repair For Omega-regular Properties

论文作者

Dave, Vrunda, Krishna, Shankara Narayanan, Murali, Vishnu, Trivedi, Ashutosh

论文摘要

本文提出了一个基于优化的框架,以自动化系统维修与欧米茄规范属性的维修。在拟议的最佳维修形式化中,该系统被表示为Kripke结构,属性为$ω$ - 规则的语言,而维修空间则表示为维修机器 - 加权的欧米茄规范传感器,配备了Büchi条件 - 重写字符串并将其与这些重写相关联。为了将最终的成本序列转换为易于解释的收益,我们考虑了几个聚合功能,以将成本序列映射到数字(包括限制上级,超级,折扣价和平均值),以定义定量成本语义。因此,最佳维修的问题是确定当允许的成本受给定阈值界限时,是否可以重写给定系统的迹线以满足$ω$的属性。我们还考虑了损害验证的双重挑战,即假定在某些给定的成本限制下重写对抗的重写,并要求确定系统的所有痕迹是否满足规格,而不管重写的重写如何。由于损害验证问题的负面结果,我们研究了设计最小的Kripke结构掩模的问题,以使所产生的痕迹满足阈值结合的损害,但仍满足规格。我们将这个问题视为面具综合问题。本文介绍了自动机理论解决方案,以修复限制,超级,折扣和平均成本语义的限制,损害验证和掩模合成问题。

This paper presents an optimization based framework to automate system repair against omega-regular properties. In the proposed formalization of optimal repair, the systems are represented as Kripke structures, the properties as $ω$-regular languages, and the repair space as repair machines -- weighted omega-regular transducers equipped with Büchi conditions -- that rewrite strings and associate a cost sequence to these rewritings. To translate the resulting cost-sequences to easily interpretable payoffs, we consider several aggregator functions to map cost sequences to numbers -- including limit superior, supremum, discounted-sum, and average-sum -- to define quantitative cost semantics. The problem of optimal repair, then, is to determine whether traces from a given system can be rewritten to satisfy an $ω$-regular property when the allowed cost is bounded by a given threshold. We also consider the dual challenge of impair verification that assumes that the rewritings are resolved adversarially under some given cost restriction, and asks to decide if all traces of the system satisfy the specification irrespective of the rewritings. With a negative result to the impair verification problem, we study the problem of designing a minimal mask of the Kripke structure such that the resulting traces satisfy the specifications despite the threshold-bounded impairment. We dub this problem as the mask synthesis problem. This paper presents automata-theoretic solutions to repair synthesis, impair verification, and mask synthesis problem for limit superior, supremum, discounted-sum, and average-sum cost semantics.

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