The Complexity of Synthesizing nop-Equipped Boolean Nets from g-Bounded Inputs (Technical Report)

TL;DR

This paper investigates the computational complexity of synthesizing nop-equipped Boolean Petri nets from graphs with bounded in-degree and out-degree, providing insights into the problem's difficulty based on the parameter g.

Contribution

It characterizes the complexity of synthesizing nop-equipped Boolean Petri nets from graphs with bounded degree for any fixed g, advancing understanding of the synthesis problem.

Findings

Complexity depends on the bound g of the graph degrees.

For fixed g, the synthesis problem's complexity is characterized.

Results inform the feasibility of net synthesis from bounded graphs.

Abstract

Boolean Petri nets equipped with nop allow places and transitions to be independent by being related by nop. We characterize for any fixed natural number g the computational complexity of synthesizing nop-equipped Boolean Petri nets from labeled directed graphs whose states have at most g incoming and at most g outgoing arcs.