Decidability of properties of timed arc petri nets pdf

Properties of distributed timedarc petri nets request pdf. Analysis of placetransition nets with timed arcs and its application to batch process control. Time petri nets tpn mer74 and timed petri nets wal83 are two incomparable classes of concurrent models with timing constraints. Properties of distributed time arc petri nets core. In bounded tpns, many generic properties are decidable and temporal model. Thus, we could think that this model does not increase. In spite of the fact that reachability is decidable for untimed petri nets 37, it is undecidable for timed arc petri nets 47, even for nets without any transportinhibitor arcs and age invariants. Pdf properties of distributed time arc petri nets researchgate. Petri nets are introduced from its basics and their use for modelling and veri cation of systems is discussed.

Several application domains are selected to illustrate the method. Performance evaluation of asynchronous concurrent systems by. Citeseerx document details isaac councill, lee giles, pradeep teregowda. This paper aims to apply the tctl model checking techniques to time petri nets.

This book intends to bridge the gap between petri nets, which ful l many desirable requirements, and the systems modelling and implementation process. This variant, called timed arc petri nets, enjoys decidability of coverability 1, but cannot. We discuss pt nets where the arc cardinalities are allowed to be markingdependent expressions of various types, resulting in a hi. Among timed petri nets, time can be considered relative to places or transitions sif80, py99. Decidability of properties like reachability, liveness or deadlockfreeness of the autonomous model is studied in section 3. The algorithm computes optimized maximum constants for each. We collect results on the decidability of important properties, equivalence notions, and temporal logics. A variant of timed arc petri nets with place invariants is proposed in the tapaal tool 10.

Timedtransition petri nets tpns 22 and timedarc petri nets 26. Towards a notion of distributed time for petri nets core. This variant, called timed arc petri nets, enjoys decidability of coverability 9, but cannot impose urgent ring, which is a key issue in real time systems. Tpns can constrain each transition with a timing interval. Keeping one global clock synchronised is usually the bottleneck of a processor design. Decidability of properties of timedarc petri nets e. Decidability of properties of timedarc petri nets eprints. Verification of liveness properties on closed timedarc. Pdf on nondecidability of reachability for timedarc. We present an algorithm for liveness analysis of closed timed arc petri nets tapn extended with weights, transport arcs, inhibitor arcs and age invariants and prove its correctness.

Decidability and complexity of petri net problems an. It is well known that the reachability problem is undecidable for petri nets with ordered data, while. On the other hand, in the model of timedarc petri nets 5. Partialorder semantics have been considered in the timed setting. Recently, 2 considers variants of time and timedarc petri nets with urgency tpnus, where decidability of reachability and coverability is obtained by restricting urgency to tran sitions consuming tokens only from bounded places. H undecidability of coverability and boundedness for timedarc petri nets with invariants. There exist close connections between timed petri nets, petri nets with one inhibitor arc, and transfer nets. Minimal cost reachabilitycoverability in priced timed. Note that semilinearity of the reachability set reachn does. With these properties, a run of s can be defined as a finite sequence of moves. A timed execution of a discrete event system des is a finite or infinite sequence of events.

Our goal, then, in this paper is to present an automatic translation of specifications written in a timed algebraic language tpal into a timed model of petri nets timedarc petri nets. Each place has exactly one input transition and exactly one output transition deterministic timed petri nets. Timedarc petri nets tapn s are not turing powerful, because, in particular, they cannot simulate a counter with zero testing. Pdf timedarc petri nets tapn are an extension of the classical pt nets with. Decidability of properties of timed arc petri nets. From performance evaluation to observation and control, in g. Petri net languages, models of computation related to petm nets, and some extensions and. Petri net a petri net structure is a directed weighted bipartite graph n p,t, a,w where p is the.

By using tacpn we want to minimize the updating time between two con. In the tapaal tool we consider timed arc petri nets tapn 4, 7 where. Several timed extensions of petri nets have been defined to capture some additional aspects, concerning with the behaviour in time of the described systems. This variant, called timed arc petri nets, enjoys decidability of coverability 1, but cannot impose urgent. In this paper we illustrate the use of timed arc petri nets for the modelling of timed concurrent systems, using the mpeg2 video encoder as an example. Properties of distributed timedarc petri nets springerlink. Translating tpal specifications into timedarc petri nets. The freechoice assumption in this paper is orthogonal to this approach and it would be interesting to see how it a ects decidability for tpnus. Finally, we show that if we allow negative costs then even the cost threshold coverability problem for ppns becomes undecidable. On non decidability of reachability for timed arc petri nets. If an arc is directed from node i to node j either from a place to a.

Tapn and section 5 explains the main decidability and complexity results. Pdf verification of timedarc petri nets researchgate. Here are some classes of petri nets and counter systems for which the reachability relation. A recent overview aiming at a comparison of the di erent time dependent models including timed automata is given in 15. Therefore in this thesis we propose timed arc colored petri net tacpn an extension to petri net, combing the coloured petri nets and timed arc petri nets 11. To the best of our knowledge, the explicit methods have not yet been employed in the verification of liveness properties in petri net models extended with time. Timedarc petri nets tapns are not turing powerful, because, in particular, they cannot simulate a counter with zero testing. Editor, simulator and veri er of timedarc petri nets. The two main time extensions of petri nets are time petri nets tpn 33 and timed petri nets 37. Disc11, june 9th 2011 1 time and petri nets 2 timed models 3 expressiveness 4 analysis. Veri cation of liveness properties on closed timedarc. A collection of 10 rules of thumb is presented that helps to determine the decidability and complexity of a large number of petri net problems. Decidability of properties of timedarc petri nets core. In section 8 we establish a connection between a subclass.

Pre and post logical conditions of event occurrence. Citeseerx decidability of properties of timedarc petri nets. The reachability problem for local timedarc petri nets can be formulated as follows. Decidability of properties of timedarc petri nets springerlink. However, decidability of all the behavioral properties mentioned above has not been studied in timed arc petri nets to the same extent as in regular petri nets. Specification and analysis of the mpeg2 video encoder. Section 4 deals with the timed model, proving that timed continuous petri nets and timed di. We consider unbounded timed petri nets tpns where each token is equipped with a realvalued clock representing the age of the token. Stochastic time delays with transitions color petri nets. Each arc in the net is provided with a subinterval of the natural numbers, restricting the ages of the tokens travelling the arc. We survey 25 years of research on decidability issues for petri nets. Notice that this contrasts with the result by mayr 10 stating the decidability of reachability for ordinary petri nets.

Foundations of software technology and theoretical computer science. Timed arc petri nets tapns are not turing powerful, because, in particular, they cannot simulate a counter with zero testing. Petri nets is undecidable 26, even in the case where tokens in different places. Timedarc petri nets tapn are an extension of the classical pt nets with continuous time. Application of timedarc colored petri net for network. However the petri net model lacks the ability to model real time systems and therefore, a timed extension of it, the timed arc petri net model, was introduced. Ttpns and ptpns, but both classes of timed petri nets are included in both p.