Formal analysis of timed continuous Petri nets

In this paper, we develop an automated framework for formal verification of timed continuous Petri nets (contPN). Specifically, we consider two problems: (1) given an initial set of markings, construct a set of unreachable markings, i.e., such that all trajectories starting in the initial set avoid the latter one; (2) given a linear temporal logic (LTL) formula over a set of linear predicates in the state, construct a set of initial states such that all trajectories originating there satisfy the specification. The starting point for our approach is the observation that a contPN system can be written as a piecewise affine (PWA) system with a polyhedral partition. We propose an iterative method for analysis of PWA systems from specifications given as LTL formulas over linear predicates. The computation consists of polyhedral operations and searches on graphs only. We present two illustrative numerical examples.