On the Complexity of Techniques That Make Transition Systems Implementable by Boolean Nets

TL;DR

This paper investigates the computational complexity of modifying transition systems to make them implementable by Boolean nets, showing many related problems are NP-complete.

Contribution

It establishes NP-completeness results for various modification problems in synthesizing Boolean nets from transition systems.

Findings

Most modification problems are NP-complete.

NP-completeness holds for flip-flop nets and derivatives.

Complexity results guide the limits of feasible synthesis techniques.

Abstract

Synthesis consists in deciding whether a given labeled transition system (TS) $A$ can be implemented by a net $N$ of type $\tau$. In case of a negative decision, it may be possible to convert $A$ into an implementable TS $B$ by applying various modification techniques, like relabeling edges that previously had the same label, suppressing edges/states/events, etc. It may however be useful to limit the number of such modifications to stay close to the original problem, or optimize the technique. In this paper, we show that most of the corresponding problems are NP-complete if $\tau$ corresponds to the type of flip-flop nets or some flip-flop net derivatives.