A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

TL;DR

This paper introduces a new forward reachability algorithm for bounded Timed-arc Petri Nets, enhancing verification efficiency with novel reduction techniques and implementation in TAPAAL, outperforming existing methods.

Contribution

The paper presents a direct DBM-based reachability algorithm for bounded TAPNs with transport, inhibitor, and age invariants, including correctness proofs and a new state-space reduction method.

Findings

Algorithm implemented in TAPAAL shows improved performance.

Correctness proven with symmetry and extrapolation techniques.

State-space reduction maintains soundness with age invariants and inhibitor arcs.

Abstract

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.