On Petri Nets with Hierarchical Special Arcs
نویسندگان
چکیده
We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy on places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also investigate what happens when we have a mix of these special arcs, some of which respect the hierarchy, while others do not. We settle the decidability status of the above four problems for all combinations of hierarchy, inhibitor, reset and transfer arcs, except the termination problem for two combinations. For both these combinations, we show that the termination problem is as hard as deciding positivity for linear recurrent sequences — a long-standing open problem.
منابع مشابه
Snoopy - A Tool to Design and Execute Graph-Based Formalisms
We sketch the fundamental properties and features of Snoopy, a tool to model and execute (animate, simulate) hierarchical graph-based system descriptions. The tool comes along with several pre-fabricated graph classes, especially some kind of Petri nets and other related graphs, and facilitates a comfortable integration of further graph classes due to its generic design. To support an aspect-or...
متن کاملColoured Petri Nets Extended with Place Capacities, Test Arcs and Inhibitor Arcs
In this paper we show how to extend Coloured Petri Nets (CP-nets), with three new modelling primitives—place capacities, test arcs and inhibitor arcs. The new modelling primitives are introduced to improve the possibilities of creating models that are on the one hand compact and comprehensive and on the other hand easy to develop, understand and analyse. A number of different place capacity and...
متن کاملOn the expressive power of Petri nets with transfer arcs vs. Petri nets with reset arcs
In this paper, we revisit the conjecture of [1], stating that ε-free Petri nets with transfer arcs are strictly more expressive than ε-free Petri nets with reset arcs. In [1], an ε-free Petri net with transfer arcs is provided, whose language is conjectured not to be recognizable by any ε-free Petri net with reset arcs. We show that this latter conjecture is flawed, by exhibiting an ε-free Petr...
متن کاملReconstructing X'-deterministic extended Petri nets from experimental time-series data X'
This work aims at reconstructing Petri net models for biological systems from experimental time-series data X ′. The reconstructed models shall reproduce the experimentally observed dynamic behavior in a simulation. For that, we consider Petri nets with priority relations among the transitions and control-arcs, to obtain additional activation rules for transitions to control the dynamic behavio...
متن کاملSmall Universal Deterministic Petri Nets with Inhibitor Arcs
This paper describes a series of small universal Petri nets with inhibitor arcs. Four parameters of descriptional complexity are considered: the number of places, transitions, inhibitor arcs, and the maximal degree of a transition. A number of techniques for reducing the values of these parameters, with special attention on places, are presented: we describe strongly universal Petri nets with 3...
متن کامل