Symbolic Analysis and Parameter Synthesis for Time Petri Nets Using Maude and SMT Solving

TL;DR

This paper introduces a formal analysis framework for parametric time Petri nets with inhibitor arcs using Maude and SMT solving, enabling efficient parameter synthesis and model checking.

Contribution

It presents a new symbolic rewriting logic semantics for PITPNs and integrates Maude with SMT solving for sound, complete, and more efficient analysis.

Findings

Outperforms Roméo in several benchmarks

Supports parameter synthesis from initial markings

Enables full LTL model checking with user-defined strategies

Abstract

Parametric time Petri nets with inhibitor arcs (PITPNs) support flexibility for timed systems by allowing parameters in firing bounds. In this paper we present and prove correct a concrete and a symbolic rewriting logic semantics for PITPNs. We show how this allows us to use Maude combined with SMT solving to provide sound and complete formal analyses for PITPNs. We develop a new general folding approach for symbolic reachability that terminates whenever the parametric state-class graph of the PITPN is finite. We explain how almost all formal analysis and parameter synthesis supported by the state-of-the-art PITPN tool Rom\'eo can be done in Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments on three benchmarks show that our methods outperform Rom\'eo in many cases.