Simulating Petri nets with Boolean Matrix Logic Programming

TL;DR

This paper introduces Boolean Matrix Logic Programming (BMLP), a novel method that enables efficient simulation of Petri nets within logic programming, significantly outperforming existing Prolog systems.

Contribution

The paper presents BMLP, a new approach using boolean matrices for simulating Petri nets in Prolog, with algorithms that transform nets into datalog programs for faster evaluation.

Findings

BMLP algorithms evaluate Petri nets 40 times faster than traditional Prolog systems.

BMLP enables efficient simulation and analysis of elementary Petri nets.

The approach broadens the application scope of logic programming in complex system simulation.

Abstract

Recent attention to relational knowledge bases has sparked a demand for understanding how relations change between entities. Petri nets can represent knowledge structure and dynamically simulate interactions between entities, and thus they are well suited for achieving this goal. However, logic programs struggle to deal with extensive Petri nets due to the limitations of high-level symbol manipulations. To address this challenge, we introduce a novel approach called Boolean Matrix Logic Programming (BMLP), utilising boolean matrices as an alternative computation mechanism for Prolog to evaluate logic programs. Within this framework, we propose two novel BMLP algorithms for simulating a class of Petri nets known as elementary nets. This is done by transforming elementary nets into logically equivalent datalog programs. We demonstrate empirically that BMLP algorithms can evaluate these programs 40 times faster than tabled B-Prolog, SWI-Prolog, XSB-Prolog and Clingo. Our work enables the efficient simulation of elementary nets using Prolog, expanding the scope of analysis, learning and verification of complex systems with logic programming techniques.