New Efficient Petri Net Reductions for Parallel Programs Verification

Structural model abstraction is a powerful technique for reducing the complexity of a state based enumeration analysis. We present in this paper new efficient Petri nets reductions. First, we define "behavioural" reductions (i.e. based on conditions related to the language of the net) which preserve a fundamental property of a net (i.e. liveness) and any formula of the (action-based) linear time logic that does not observe reduced transitions of the net. We show how to replace these conditions by structural or algebraical ones leading to reductions that can be efficiently checked and applied whereas enlarging the application spectrum of the previous reductions. At last, we illustrate our method on a significant and typical example of a synchronisation pattern of parallel programs.ou