Formal Verification of Stochastic Max-Plus-Linear Systems

Abstract

This work investigates the computation of finite abstractions of Stochastic Max-Plus-Linear (SMPL) systems and their formal verification against general bounded-time linear temporal specifications. SMPL systems are probabilistic extensions of discrete-event MPL systems, which are widely employed for modeling engineering systems dealing with practical timing and synchronization issues. Departing from the standard existing approaches for the analysis of SMPL systems, we newly propose to construct formal, finite abstractions of a given SMPL system: the SMPL system is first re-formulated as a discrete-time Markov process, then abstracted as a finite-state Markov Chain (MC). The derivation of precise guarantees on the level of the introduced formal approximation allows us to probabilistically model check the obtained MC against bounded-time linear temporal specifications (which are of rather general applicability), and to reliably export the obtained results over the original SMPL system. The approach is practically implemented on a dedicated software and is elucidated and run over numerical examples.