Timedtransition petri nets tpns 22 and timedarc petri nets 26. Citeseerx decidability of properties of timedarc petri nets. We discuss pt nets where the arc cardinalities are allowed to be markingdependent expressions of various types, resulting in a hi. Several timed extensions of petri nets have been defined to capture some additional aspects, concerning with the behaviour in time of the described systems. Properties of distributed timedarc petri nets request pdf. 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. In contrast to elementary petri net systems roen98, in pt nets a place can hold any number of tokens. Timedarc petri nets tapns are not turing powerful, because, in particular, they cannot simulate a counter with zero testing. Specification and analysis of the mpeg2 video encoder. Pdf verification of timedarc petri nets researchgate. If an arc is directed from node i to node j either from a place to a. Decidability and complexity of petri net problems an. Pdf on nondecidability of reachability for timedarc.
A petri net is a directed bipartite graph, in which the nodes represent transitions i. Petri net languages, models of computation related to petm nets, and some extensions and. We shall analyse timedarc petri nets 3, 7, a time extension. Timedarc petri nets tapn s are not turing powerful, because, in particular, they cannot simulate a counter with zero testing. We survey 25 years of research on decidability issues for petri nets. An algorithm for the general petri net reachability problem preliminary version. Thus, we could think that this model does not increase significantly the expressiveness of untimed petri nets. Ttpns and ptpns, but both classes of timed petri nets are included in both p. Properties of distributed timedarc petri nets springerlink. Each place has exactly one input transition and exactly one output transition deterministic timed petri nets. Decidability of properties of timedarc petri nets springerlink. Several application domains are selected to illustrate the method. Finally, we show that if we allow negative costs then even the cost threshold coverability problem for ppns becomes undecidable.
This book intends to bridge the gap between petri nets, which ful l many desirable requirements, and the systems modelling and implementation process. We collect results on the decidability of important properties, equivalence notions, and temporal logics. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Foundations of software technology and theoretical computer science. Timedarc petri nets tapn are an extension of the classical pt nets with continuous time.
Veri cation of liveness properties on closed timedarc. Decidability of properties of timedarc petri nets eprints. By using tacpn we want to minimize the updating time between two con. Pre and post logical conditions of event occurrence. 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.
Decidability of properties of timedarc petri nets core. 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. The reachability problem for local timedarc petri nets can be formulated as follows. 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. Decidability of properties of timedarc petri nets e. Petri nets for systems engineering untiredwithloving. Pdf properties of distributed time arc petri nets researchgate.
A timed execution of a discrete event system des is a finite or infinite sequence of events. It is well known that the reachability problem is undecidable for petri nets with ordered data, while. Deterministic time delays with transitions stochastic timed petri nets. On the other hand, in the model of timedarc petri nets 5. Pdf timedarc petri nets tapn are an extension of the classical pt nets with. Thus, we could think that this model does not increase. Petri nets is undecidable 26, even in the case where tokens in different places. Verification of liveness properties on closed timedarc. There exist close connections between timed petri nets, petri nets with one inhibitor arc, and transfer nets. In the tapaal tool we consider timed arc petri nets tapn 4, 7 where. Tpns can constrain each transition with a timing interval.
Decidability of properties of timed arc petri nets. Section 4 deals with the timed model, proving that timed continuous petri nets and timed di. Application of timedarc colored petri net for network. Tapn and section 5 explains the main decidability and complexity results.
Partialorder semantics have been considered in the timed setting. The two main time extensions of petri nets are time petri nets tpn 33 and timed petri nets 37. 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. 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. Keeping one global clock synchronised is usually the bottleneck of a processor design. 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. Notice that this contrasts with the result by mayr 10 stating the decidability of reachability for ordinary petri nets. Editor, simulator and veri er of timedarc petri nets. This variant, called timed arc petri nets, enjoys decidability of coverability 1, but cannot. Petri nets are introduced from its basics and their use for modelling and veri cation of systems is discussed. Among timed petri nets, time can be considered relative to places or transitions sif80, py99. Pdf decidability of safety properties of timed multiset. Decidable classes of unbounded petri nets with time and. A recent overview aiming at a comparison of the di erent time dependent models including timed automata is given in 15.
Decidability of properties like reachability, liveness or deadlockfreeness of the autonomous model is studied in section 3. A variant of timed arc petri nets with place invariants is proposed in the tapaal tool 10. This variant, called timed arc petri nets, enjoys decidability of coverability 1, but cannot impose urgent. Here are some classes of petri nets and counter systems for which the reachability relation. Properties of distributed time arc petri nets core. Towards a notion of distributed time for petri nets core. System modelling with petri nets andrea bobbio istituto elettrotecnico nazionale galileo ferraris strada delle cacce 91, 105 torino, italy reprinted from. A petri net, also known as a placetransition pt net, is one of several mathematical modeling languages for the description of distributed systems. Extensions of petri nets event graph marked graph, decisionfree. Petri net a petri net structure is a directed weighted bipartite graph n p,t, a,w where p is the. From performance evaluation to observation and control, in g. In bounded tpns, many generic properties are decidable and temporal model.
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. Stochastic time delays with transitions color petri nets. 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. 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. Timed arc petri nets tapns are not turing powerful, because, in particular, they cannot simulate a counter with zero testing. Minimal cost reachabilitycoverability in priced timed. In section 8 we establish a connection between a subclass. On non decidability of reachability for timed arc petri nets.
The algorithm computes optimized maximum constants for each. The two corresponding subclasses namely p timed petri nets and t timed petri nets are expressively equivalent sif80, py99. H undecidability of coverability and boundedness for timedarc petri nets with invariants. This paper aims to apply the tctl model checking techniques to time petri nets. Performance evaluation of asynchronous concurrent systems by. We consider unbounded timed petri nets tpns where each token is equipped with a realvalued clock representing the age of the token. 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.
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. 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. Each arc in the net is provided with a subinterval of the natural numbers, restricting the ages of the tokens travelling the arc.
1102 1060 1361 83 287 823 795 139 547 547 1278 672 899 449 25 894 576 298 594 631 597 631 34 229 834 954 1430 1084 1406 1049 525