On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency (Technical Report)
share
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 τ-synthesis (DRτS) where each place of N can influence and be influenced by at most d transitions. For a type τ, if τ-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.
READ FULL TEXT