Computation of Elementary Siphons in Petri Nets For Deadlock Control

When designing liveness-enforcing Petri net supervisors, unlike other techniques, Li et al. added control places and arcs to a plant net model for its elementary siphons only, greatly reducing the structural complexity of the controlled system. Their method, however, suffers from the expensive computation of siphons. We propose a new T-characteristic vector ζ to compute strict minimal siphons (SMS) for S3PR (systems of simple sequential processes with resources) in an algebraic fashion. For a special subclass of S3PR, called S4PR (simple S3PR), we discover that elementary siphons can be constructed from elementary circuits where all places are resources. Thus, the set of elementary siphons can be computed without the knowledge of all SMS. We also propose to construct characteristic T-vectors η by building a graph to find dependent siphons without their computations.