自动机和Petri网的临界可观测性
Critical Observability for Automata and Petri Nets
AI总结：
本文研究了自动机和Petri网模型中临界可观测性问题的计算复杂性，证明了对于有限状态自动机，该问题在NL完全；对于自动机网络，问题在PSPACE完全；而对于标记化Petri网，问题不可判定，但当临界状态集为有限或余有限时，问题变得可判定且与Petri网的不可达性问题等难。
摘要：
临界可观测性是具有物理系统的一种属性，用于检测当前状态是否属于一组临界状态。在安全关键应用中，临界状态模型可能不安全或具有特别关注的操作。De Santis等人将临界可观测性引入线性切换系统，Pola等人将其适应于离散事件系统，专注于算法复杂性。我们研究了决定自动机和Petri网模型中临界可观测性的计算复杂性。我们证明，决定临界可观测性对于有限状态自动机是（i）NL完全的，即可以在并行计算机上高效验证；对于自动机网络，问题（ii）是PSPACE完全的，即非常不可能在多项式时间内解决；而对于标记化Petri网，问题不可判定，但当临界状态（标记）集为有限或余有限时，问题变得可判定，此时问题的难度与Petri网的不可达性问题相同。
英文摘要：
Critical observability is a property of cyber-physical systems to detect whether the current state belongs to a set of critical states. In safety-critical applications, critical states model operations that may be unsafe or of a particular interest. De Santis et al. introduced critical observability for linear switching systems, and Pola et al. adapted it for discrete-event systems, focusing on algorithmic complexity. We study the computational complexity of deciding critical observability for systems modeled as (networks of) finite-state automata and Petri nets. We show that deciding critical observability is (i) NL-complete for finite automata, that is, it is efficiently verifiable on parallel computers, (ii) PSPACE-complete for networks of finite automata, that is, it is very unlikely solvable in polynomial time, and (iii) undecidable for labeled Petri nets, but becoming decidable if the set of critical states (markings) is finite or co-finite, in which case the problem is as hard as the non-reachability problem for Petri nets.
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