Two decades ago, Alur, Henzinger, and Vardi introduced the reachability problem for parametric timed automata in the seminal paper [2]. Their main results are that reachability is decidable for timed automata with a single parametric clock, and undecidable for timed automata with three or more parametric clocks. In the case of two parametric clocks, decidability was left open, with hardly any p...

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...

We show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gi...

Coloured Petri nets are well suited to the modelling of symmetric systems. Model symmetries can be usefully exploited for the sake of analysis efficiency as well as for modelling convenience. We present a reduced reachability graph called symbolic reachability graph that enjoys the following properties: (1) it can be constructed directly by an efficient algorithm without considering the actual ...

The reachability sets of Vector Addition Systems of dimension six or more can be non-semilinear. This may be one reason why the inclusion problem (as well as the equality problem) for reachability sets of vector addition systems in general is undecidable, even though the reachability problem itself is known to be decidable. We show that any one-dimensional projection of the reachability set of ...

The successful deployment of multicast in the Internet requires the availability of good network management solutions. One of the first management tasks for multicast is to verify its availability in the network. This task is usually referred to as reachability monitoring. Reachability ensures that sources can reach all existing and potential group members. Reachability also implies that receiv...

In this paper, we focus on the symmetrical relationship between multi-properties objective reachability problems and multi-objective sets over FKS based Zadeh logic. First, give formal definitions of those two problems. Then, study their relationships find that a problem special case have symmetry. Finally, polynomial time algorithm symmetry to convert problem. addition, an illustrative example...

We present a structure for transition systems with which the main decidability results on Petri nets can be generalized to structured transition systems. We define the reduced reachability tree of a structured transition system; it allows one to decide the finite reachability tree problem (also called the finite termination problem) and the finite reachability set problem. A general definition ...

The reachability problem for graphs is a key problem in understanding the power of various logarithmic space complexity classes. For example, the reachability problem for directed graphs is logspace-complete for the complexity class NspAcE(log n) [5] and hence the open question DSPACE(log n) = NSPACE(log n) can be settled by answering whether this reachability problem belongs to DsPAcE(log n). ...