SMT Formulae of Preemptive Controlled Timed Petri Nets and its Application to Distributed Mediators

Abstract

Preemption is useful technique in real-time systems and several extensions of Merlin's time Petri net have been proposed to model the preemption. However, in timed Petri nets, the modeling of the preemption has not been studied. On the other hand, by optimization of a SAT/SMT solver, large scale problems are solvable in a realistic computation time by using a SAT/SMT formulation. In this paper, first, we define preemptive controlled timed Petri nets abbreviated as pCTdPNs, where the control of the preemption is done by external input places. Next, we represent their dynamics using SMT formulae. Finally, we apply pCTdPNs to modeling of distributed mediators with several tasks executed by multi-processor systems, and obtain a task assignment to each processor and task scheduling using an SMT solver.