Resource Allocation Systems: Some Complexity Results on the S4PR Class

In recent times, Petri nets have consolidated as a powerful formalism for the analysis and treatment of deadlocks in Resource Allocation Systems (RAS). In particular, the methodological framework yielded by the SPR class has raised considerable interest on the grounds of a well-balanced compromise between modelling flexibility and the provision of sound and effective correction techniques. These are strengthened by the advantages of the abstraction process, which allows the effective application of these techniques to diverse application domains. Most of the works on this class focus on providing tools and algorithms for dealing with the so-called resource allocation problem. This paper takes a different approach to provide an insight into the inherent computational complexity of the problem, from the perspective of optimality in either prevention, avoidance or detection of deadlocks. In particular, we will prove that most of the problems involved fall within the category of NP or co-NP-complete problems.