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An Upper Bound for the Reachability Problem of Safe, Elementary Hornets

Köhler-Bußmeier M., Heitmann F.

Fundamenta Informaticae

2016

Vol. 143, nr 1/2

89--100

In this paper we study the complexity of the reachability problem HORNETS, an algebraic extension of object nets. Here we consider the restricted class of safe, elementary HORNETS. In previouswork we established the lower bound, i.e. reachability requires at least exponential space. In another work we have shown we can simulate elementary HORNETS with elementary object nets EOS, where reachability is known to be PSpace-complete. Since this simulation leads to a double exponential increase in the size of the simulating EOS, we obtain that for HORNETS the reachability problem is solvable in double exponential space. In this contributionwe show that this kind of simulation is rather bad, since we show that exponential space is sufficient. Together with the known lower bound this shows that the upper is tight.

Structural and Dynamic Restrictions of Elementary Object Systems

Heitmann F., Köhler-Bußmeier M.

Fundamenta Informaticae

2014

Vol. 135, nr 4

387--401

Elementary object systems (EOS for short) are Petri nets in which tokens may be Petri nets again. Originally proposed by Valk for a two levelled structure, the formalism was later generalised for arbitrary nesting structures. However, even if restricted to a nesting depth of two, EOS are Turing-complete and thus many problems like reachability and liveness are undecidable for them. Nonetheless, since they are useful to model many practical applications a natural question is how to restrict the formalism in such a way, that the resulting restricted formalism is still helpful in a modelling context, but so that important verification problems like reachability become quickly decidable. In the last years several structural and dynamic restrictions for EOS have therefore been investigated. These investigations have been central to the first author’s recent PhD thesis and have been published in past editions of this journal and on conferences. In this paper we add several new results and present them together with the old in a unified fashion highlighting the central message of these investigations.