Finite Abstractions of Stochastic Max-Plus-Linear Systems

This work investigates the use of finite abstractions to study the finite-horizon probabilistic invariance problem over Stochastic MaxPlus-Linear (SMPL) systems. SMPL systems are probabilistic extensions of discrete-event MPL systems that are widely employed in the engineering practice for timing and synchronisation studies. We construct finite abstractions by re-formulating the SMPL system as a discretetime Markov process, then tailoring formal abstraction techniques in the literature to generate a finite-state Markov Chain (MC), together with precise guarantees on the level of the introduced approximation. This finally allows to probabilistically model check the obtained MC against the finite-horizon probabilistic invariance specification. The approach is practically implemented via a dedicated software, and elucidated in this work over numerical examples.