A Much Compact Abstraction of the State Space of Real time Preemptive Systems

Preemptive Systems are systems whose tasks are timely constrained and which can be suspended for a while and resumed afterwards. In order to check for their reliability, formal methods are applied to model and to analyze their behaviors. This is achieved by computing their state spaces that can be abstracted and encoded as graphs. We present in this paper an algorithm allowing an efficient computation of a DBM over-approximation of the state space of preemptive systems modeled by using Time Petri Nets with inhibitor arcs. For this effect, each class of this graph is expressed as a pair (M, D), where M is a marking and D is the system of DBM inequalities. In [1] we have defined an algorithm to compute the system D straightforwardly in its normal form, without requiring computing the intermediary polyhedron. We explore for this abstraction a suitable equivalence relation that contracts yet more the graphs. Experimental results comparing our algorithm with other approaches are reported.