Undecidability of Coverability and Boundedness for Timed-Arc Petri Nets with Invariants
نویسندگان
چکیده
Timed-Arc Petri Nets (TAPN) is a well studied extension of the classical Petri net model where tokens are decorated with real numbers that represent their age. Unlike reachability, which is known to be undecidable for TAPN, boundedness and coverability remain decidable. The model is supported by a recent tool called TAPAAL which, among others, further extends TAPN with invariants on places in order to model urgency. The decidability of boundedness and coverability for this extended model has not yet been considered. We present a reduction from two-counter Minsky machines to TAPN with invariants to show that both the boundedness and coverability problems are undecidable.
منابع مشابه
Decidable Classes of Unbounded Petri Nets with Time and Urgency
Adding real time information to Petri net models often leads to undecidability of classical verification problems such as reachability and boundedness. For instance, models such as Timed-Transition Petri nets (TPNs) [22] are intractable except in a bounded setting. On the other hand, the model of TimedArc Petri nets [26] enjoys decidability results for boundedness and control-state reachability...
متن کاملDecidability and complexity of Petri nets with unordered data
We prove several decidability and undecidability results for ν-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of ν-PN strictly surpasses that of P/T nets. We encode ν-PN into Petri Data Nets, so that coverability, termination...
متن کاملDense-Timed Petri Nets: Checking Zenoness, Token liveness and Boundedness
We consider Dense-Timed Petri Nets (TPN), an extension of Petri nets in which each token is equipped with a real-valued clock and where the semantics is lazy (i.e., enabled transitions need not fire; time can pass and disable transitions). We consider the following verification problems for TPNs. (i) Zenoness: whether there exists a zeno-computation from a given marking, i.e., an infinite compu...
متن کاملDecision Problems for Petri Nets with Names
We prove several decidability and undecidability results for ν-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of ν-PN strictly surpasses that of P/T nets. We prove that ν-PN are Well Structured Transition Systems. In particul...
متن کاملProperties of Distributed Timed-Arc Petri Nets
In [12] we started a research on a distributed-timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. This formalism enables to model e.g. hardware architectures like GALS. We give a formal definition of process semantics for our model and investigate several properties of local versus globa...
متن کامل