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Time Petri Nets State Space Reduction Using Dynamic Programming
"... Abstract. In this paper a parametric description for the state space of an arbitrary TPN is given. An enumerative procedure for reducing the state space is introduced. The reduction is defined as a truncated multistage decision problem and solved recursively. A reachability graph is defined in a dis ..."
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Abstract. In this paper a parametric description for the state space of an arbitrary TPN is given. An enumerative procedure for reducing the state space is introduced. The reduction is defined as a truncated multistage decision problem and solved recursively. A reachability graph is defined in a discrete way by using the reachable integerstates of the TPN.
Modelling and analysis of biochemical networks with time petri nets
 In 13th Int. Workshop on Concurrency Specification and Programming (CS&P’04), number 170 in Informatik–Berichte
, 2004
"... Biochemical networks are modelled at different abstraction levels. It is common sense to differentiate between quantitative (kinetic) models and qualitative (stoichiometric or even purely causal) models. The longterm objective of quantitative models is to predict the systems ’ dynamic behaviour. Th ..."
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Biochemical networks are modelled at different abstraction levels. It is common sense to differentiate between quantitative (kinetic) models and qualitative (stoichiometric or even purely causal) models. The longterm objective of quantitative models is to predict the systems ’ dynamic behaviour. They are commonly used
On Performance Bounds for Interval Time Petri Nets
 Enschede (The Netherlands
, 2004
"... Interval time Petri Nets are Petri nets in which time intervals are associated to transitions. Their quantitative analysis basically consists in applying enumerative techniques that suffer the well known state space explosion problem. To overcome this problem several methods have been proposed in th ..."
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Cited by 4 (2 self)
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Interval time Petri Nets are Petri nets in which time intervals are associated to transitions. Their quantitative analysis basically consists in applying enumerative techniques that suffer the well known state space explosion problem. To overcome this problem several methods have been proposed in the literature, that either allow to obtain equivalent nets with a reduced state space or avoid the construction of the whole state space. The alternative method proposed here consists in computing performance bounds to partially characterize the quantitative behavior of interval time Petri Nets by exploiting their structural properties and/or by applying operational laws. The performance bound computation is not a new technique: it has been proposed for timed Petri nets. In this paper we present the results obtained from a preliminary investigation on the applicability of bounding techniques of timed Petri nets to interval time Petri Nets. 1.
TimeIndependent Liveness in Time Petri Nets
"... Petri nets have been used to describe and study concurrent systems for more than fortyfive years. At first glance, time and concurrence do not seem to have much in common. But if one looks closer, the opposite is the case. There are endless examples from different areas showing this. For this reaso ..."
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Petri nets have been used to describe and study concurrent systems for more than fortyfive years. At first glance, time and concurrence do not seem to have much in common. But if one looks closer, the opposite is the case. There are endless examples from different areas showing this. For this reason, a large variety of time dependent Petri nets have been introduced and well studied. One of the first such nets is the Time Petri net (TPN), introduced in [9]. Time Petri nets (TPN) are derived from classical Petri nets. Additionally, each transition t is associated with a time interval [at, bt]. Here at and bt are relative to the time, when t was enabled last. When t becomes enabled, it can not fire before at time units have elapsed, and it has to fire not later than bt time units unless t was disabled in between by the firing of another transition. The firing of a transition itself takes no time. The time interval is designed by real numbers, but the interval bounds are nonnegative rational numbers. It is easy to see (cf. [3]) that w.l.o.g. the interval bounds can be considered as integers only.
Verification of Nonfunctional Properties of a Composable Architecture with Petrinets
, 2001
"... In this paper, we introduce our concept of composability and present the MSS architecture as an example for a composable architecture. MSS claims to be composable with respect to timing properties. We discuss, how to model and prove properties in such an architecture with timeextended Petrinets. ..."
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In this paper, we introduce our concept of composability and present the MSS architecture as an example for a composable architecture. MSS claims to be composable with respect to timing properties. We discuss, how to model and prove properties in such an architecture with timeextended Petrinets. As a result, the rst step of a proof of composability is presented as well as a new kind of Petrinet, which is more suitable for modeling architectures like MSS.
Computation of Performance Bounds for RealTime Systems Using Time Petri Nets
 SUBMITTED TO IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS
, 2009
"... Time Petri Nets (TPNs) have been widely used for the verification and validation of realtime systems during the software development process. Their quantitative analysis consists in applying enumerative techniques that suffer the well known state space explosion problem. To overcome this problem se ..."
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Cited by 1 (0 self)
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Time Petri Nets (TPNs) have been widely used for the verification and validation of realtime systems during the software development process. Their quantitative analysis consists in applying enumerative techniques that suffer the well known state space explosion problem. To overcome this problem several methods have been proposed in the literature, that either provide rules to obtain equivalent nets with a reduced state space or avoid the construction of the whole state space. In this paper, we propose a method that consists in computing performance bounds to predict the average operational behavior of TPNs by exploiting their structural properties and by applying operational laws. Performance bound computation was first proposed for Timed (Timed PNs) and Stochastic Petri nets (SPNs). We generalize the results obtained for Timed PNs and SPNs to make the technique applicable to TPNs and their extended stochastic versions: TPN with firing frequency intervals (TPNFs) and Extended TPNs (XTPNs). Finally, we apply the proposed bounding techniques on the case study of a robotcontrol application taken from the literature.
Control and Cybernetics
"... Time Petri nets state space reduction using dynamic programming by ..."
Using Integer Time Steps for Checking Branching Time Properties of Time Petri Nets
"... Abstract. Verification of timed systems is an important subject of research, and one of its crucial aspects is the efficiency of the methods developed. Extending the result of Popova which states that integer time steps are sufficient to test reachability properties of time Petri nets [5, 8], in our ..."
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Abstract. Verification of timed systems is an important subject of research, and one of its crucial aspects is the efficiency of the methods developed. Extending the result of Popova which states that integer time steps are sufficient to test reachability properties of time Petri nets [5, 8], in our work we prove that the discretetime semantics is also sufficient to verify ECTL ∗ and ACTL ∗ properties of TPNs with the dense semantics. To show that considering this semantics instead of the dense one is profitable, we compare the results for SATbased bounded model checking of ACTL−X properties and the class of distributed time Petri nets. 1
Determining WorstCase Times of Unknown Paths in Time Petri Nets
"... Abstract. In this paper, a method to determine bestcase and worstcase times between two arbitrary markings in a bounded TPN is presented. The method uses a discrete subset of the state space of the net and achieves the results, which are integers, in polynomial time. As an application of the method ..."
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Abstract. In this paper, a method to determine bestcase and worstcase times between two arbitrary markings in a bounded TPN is presented. The method uses a discrete subset of the state space of the net and achieves the results, which are integers, in polynomial time. As an application of the method the solving of a scheduling problem is shown.
Petri Nets with Time Windows: Possibilities and Limitations
"... Abstract. In this paper we present a time extension of Petri nets called Petri net with Time Windows (short: twPN) where time intervals (windows) are associated with the places. We give a formal definition for this class and compare these time dependent Petri nets with their (timeless) skeletons. I ..."
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Abstract. In this paper we present a time extension of Petri nets called Petri net with Time Windows (short: twPN) where time intervals (windows) are associated with the places. We give a formal definition for this class and compare these time dependent Petri nets with their (timeless) skeletons. In particular, we compare their sets of reachable markings and their liveness behaviour. The sets of reachable markings are equal but the liveness behaviors are different. For a restricted class of twPNs, we give a sufficient condition for liveness equivalence. We prove that twPNs are not Turing equivalent and finally show the existence of runs with time gaps in a twPN. 1