On the Computation of Stubborn Sets of Colored Petri Nets

Abstract

Valmari’s Stubborn Sets method is a member of the so-called partial order methods. These techniques are usually based on a selective search algorithm: at each state processed during the search, a stubborn set is calculated and only the enabled transitions of this set are used to generate the successors of the state. The computation of stubborn sets requires to detect dependencies between transitions in terms of conflict and causality. In colored Petri nets these dependencies are difficult to detect because of the color mappings present on the arcs: conflicts and causality connections depend on the structure of the net but also on these mappings. Thus, tools that implement this technique usually unfold the net before exploring the state space, an operation that is often untractable in practice. We present in this work an alternative method which avoids the cost of unfolding the net. To allow this, we use a syntactically restricted class of colored nets. Note that this class still enables wide modeling facilities since it is the one used in our model checker Helena which has been designed to support the verification of software specifications. The algorithm presented has been implemented and several experiments which show the benefits of our approach are reported. For several models we obtain a reduction close or even equal to the one obtained after an unfolding of the net. We were also able to efficiently reduce the state spaces of several models obtained by an automatic translation of concurrent software.