限制依赖布尔Petri网综合的参数化复杂性
On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency
摘要：
用Petri网对现实世界的系统进行建模，可以受益于它们的并行性，同步性和冲突的通用概念，并获得简洁而富有表现力的系统表示。从一个顺序规范的网的合成算法，使完善的Petri网理论，通过一个网模型，应用于系统分析。$τ$ -合成问题在于判定给定的有向标记图$A$是否同构于$τ$型布尔Petri网$N$的可达图。在肯定决策的情况下，应构建$N$。对于许多布尔类型的网，问题是NP完全的。本文讨论了$τ$ -合成的一个特殊变体，它对目标网$N$施加了限制：我们研究了依赖性$d$ -限制的tau-合成（DR $τ$ S），其中$N$的每个位置都可以影响和被最多d个跃迁影响.对于类型$τ$，如果tau合成是NP完全的，则DR $τ$ S也是NP完全的。在本文中，我们证明了由$d$参数化的DR $τ$ S在XP中。此外，我们证明了它是W[2]-困难的，对于许多布尔类型，允许无条件的相互作用设置和重置。
英文摘要：
Modeling of real-world systems with Petri nets allows to benefit from their generic concepts of parallelism, synchronisation and conflict, and obtain a concise yet expressive system representation. Algorithms for synthesis of a net from a sequential specification enable the well-developed theory of Petri nets to be applied for the system analysis through a net model. The problem of $τ$-synthesis consists in deciding whether a given directed labeled graph $A$ is isomorphic to the reachability graph of a Boolean Petri net $N$ of type $τ$. In case of a positive decision, $N$ should be constructed. For many Boolean types of nets, the problem is NP-complete. This paper deals with a special variant of $τ$-synthesis that imposes restrictions for the target net $N$: we investigate dependency $d$-restricted tau-synthesis (DR$τ$S) where each place of $N$ can influence and be influenced by at most d transitions. For a type $τ$, if tau-synthesis is NP-complete then DR$τ$S is also NP-complete. In this paper, we show that DR$τ$S parameterized by $d$ is in XP. Furthermore, we prove that it is W[2]-hard, for many Boolean types that allow unconditional interactions set and reset.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
