2020/09/17 by Ronny Tredup, Evgeny Erofeev
Computer Science · #cs.CC
paper · pdf · doi:10.4204/eptcs.324.7
published as EPTCS 324, 2020, pp. 78-95 · In Proceedings ICE 2020, arXiv:2009.07628. arXiv admin note: substantial text overlap with arXiv:2007.12372
arxiv created 2020/09/17 · arxiv updated 2020/09/21
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 (DRτS) 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 DRτS is also NP-complete. In this paper, we show that DRτS 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.