P- and T-systems in the nets-within-nets-formalism

Abstract

We are concerned with (strongly deterministic) generalised state machines (GSMs), a restricted formalism of the nets-within-nets-family, and further restrict the involved nets to P- and T-nets. While GSMs with these restrictions are likely to be of little use in modelling applications, understanding them better might help in future attempts to analyse more sophisticated formalisms. We show that, given a strongly deterministic GSM where the system net and all object nets are P-nets, it is PSpace-complete to decide the reachability of a given marking. In past work we have already shown that the same restriction to T-nets remains solvable in polynomial time. We discuss this work in the context given here. At last we give some initial results concerning other combinations of restricting the system and/or the object nets to P- and/or T-nets. Throughout we also discuss the effect of dropping the restriction to strongly deterministic GSMs. © 2012 Springer-Verlag.