Symbolic Reachability Analysis of High Dimensional Max-Plus Linear Systems

TL;DR

This paper introduces a symbolic reachability analysis method for high-dimensional Max-Plus Linear systems using SMT solvers, significantly improving scalability and performance over existing algorithms.

Contribution

It develops an SMT-based symbolic approach for reachability analysis of MPL systems, enabling verification of models with over 100 variables, which was previously infeasible.

Findings

Outperforms existing RA algorithms in efficiency and scalability.

Enables analysis of MPL systems with more than 100 variables.

Demonstrates applicability to industrial-scale models.

Abstract

This work discusses the reachability analysis (RA) of Max-Plus Linear (MPL) systems, a class of continuous-space, discrete-event models defined over the max-plus algebra. Given the initial and target sets, we develop algorithms to verify whether there exist trajectories of the MPL system that, starting from the initial set, eventually reach the target set. We show that RA can be solved symbolically by encoding the MPL system, as well as initial and target sets into difference logic, and then checking the satisfaction of the resulting logical formula via an off-the-shelf satisfiability modulo theories (SMT) solver. The performance and scalability of the developed SMT-based algorithms are shown to clearly outperform state-of-the-art RA algorithms for MPL systems, newly allowing to investigate RA of high-dimensional MPL systems: the verification of models with more than 100 continuous variables shows the applicability of these techniques to MPL systems of industrial relevance.