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1
Content available remote Controlling Petri Net Behavior using Priorities for Transitions
Lomazova I. A., Popova-Zeugmann L.
Fundamenta Informaticae
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2016
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Vol. 143, nr 1/2
101--112
EN
In this paper we examine how it is possible to control Petri net behavior with the help of transition priorities. Controlling here means forcing a process to behave in a stable way by ascribing priorities to transitions and hence transforming a classic Petri net into a Priority Petri net. For Petri net models stability is often ensured by liveness and boundedness. These properties are crucial in many application areas, e.g. workflow modeling, embedded systems design, and bioinformatics. In this paper we study the problem of transforming a given live, but unbounded Petri net into a live and bounded one by adding priority constraints. We specify necessary conditions for the solvability of this problem and present an algorithm for ascribing priorities to net transitions in such a way that the resulting net becomes bounded while staying live.
2
Content available remote A Holistic State Equation for Timed Petri Nets
Werner M., Popova-Zeugmann L., Haustein M., Pelz E.
Fundamenta Informaticae
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2014
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Vol. 133, nr 2/3
305--322
EN
In this paper we investigate Timed Petri nets (TPN) with fixed, possibly zero, durations and maximal step semantics. We define a new state representationwhere a state is a pair of a marking for the places and a marking for the transitions (a matrix of clocks). For this representation of states we provide an algebraic state equation. Such a state equation lets us prove a sufficient condition for the non-reachability of a state in a TPN. This application of the state equation is subsequently illustrated by an example.
3
Content available remote Algebraical Characterisation of Interval-Timed Petri Nets with Discrete Delays
Popova-Zeugmann L., Pelz E.
Fundamenta Informaticae
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2012
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Vol. 120, nr 3/4
341-357
EN
In this paper we consider Interval-Timed Petri nets (ITPN) which are an extension of Timed Petri nets. They are considered to behave with discrete delays. The class of ITPNs is Turing complete and therefore the reachability of an arbitrary marking in such a net is not decidable. We introduce a time dependent state equation for a firing sequence of ITPNs, which is analogous to the state equation for a firing sequence in standard Petri nets and we prove its correctness using linear algebra. Our result is original and delivers both a necessary condition for reachability and a sufficient condition for non-reachability of an arbitrary marking in an ITPN.
4
Content available remote Time-independent Liveness in Time Petri Nets
Bachmann J.P., Popova-Zeugmann L.
Fundamenta Informaticae
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2010
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Vol. 102, nr 1
1-17
EN
In this paper we consider a class of Time Petri nets defined by structural restrictions. Each Time Petri net which belongs to this class has the property that their liveness behaviour does not depend on the time. Therefore, the Time Petri net is live when its skeleton is live.
5
Content available remote Petri Nets with TimeWindows: A Comparison to Classical Petri Nets
Wegener J-T., Popova-Zeugmann L.
Fundamenta Informaticae
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2009
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Vol. 93, nr 1-3
337-352
EN
We present Petri nets with time windows (tw-PN) where each place is associated with an interval (window). Every token which arrives at a place gets a real-valued clock which shows its "age". A transition can fire when all needed tokens are "old enough". When a token reaches an "age" equal to the upper bound of the place where it is situated, the "token's age", i.e., clock will be reset to zero. Following this we compare these time dependent Petri nets with their (timeless) skeletons. The sets of both their reachable markings are equal, their liveness behaviour is different, and neither is equivalent to Turing machines. We also prove the existence of runs where time gaps are possible in the tw-PN, which is an extraordinary feature.
6
Content available remote Time Petri nets state space reduction using dynamic programming
Popova-Zeugmann L.
Control and Cybernetics
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2006
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Vol. 35, no 3
721-748
EN
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 denned in a discrete way by using the reachable integer-states of the TPN.
7
Content available remote Time Petri Nets for Modelling and Analysis of Biochemical Networks
Popova-Zeugmann L., Heiner M., Koch I.
Fundamenta Informaticae
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2005
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Vol. 67, nr 1-3
149--162
EN
Biochemical networks are modelled at different abstraction levels. Basically, qualitative and quantitative models can be distinguished, which are typically treated as separate ones. In this paper, we bridge the gap between qualitative and quantitative models and apply time Petri nets for modelling and analysis of molecular biological systems. We demonstrate how to develop quantitative models of biochemical networks in a systematic manner, starting from the underlying qualitative ones. For this purpose we exploit the well-established structural Petri net analysis technique of transition invariants, which may be interpreted as a characterisation of the system's steady state behaviour. For the analysis of the derived quantitative model, given as time Petri net, we present structural techniques to decide the time-dependent realisability of a transition sequence and to calculate its shortest and longest time length. All steps of the demonstrated approach consider systems of integer linear inequalities. The crucial point is the total avoidance of any state space construction. Therefore, the presented technology may be applied also to infinite systems, i.e. unbounded Petri nets.
8
Content available remote Extreme Runtimes of Schedules Modelled by Time Petri Nets
Popova-Zeugmann L., Werner M.
Fundamenta Informaticae
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2005
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Vol. 67, nr 1-3
163--174
EN
In this paper, a method to determine best-case and worst-case 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 solution of a scheduling problem is shown.
9
Content available remote A Method to Prove Non-Reachability in Priority Duration Petri Nets
Werner M., Popova-Zeugmann L., Richling J.
Fundamenta Informaticae
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2004
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Vol. 61, nr 3,4
351--368
EN
Times and priorities are important concepts that are frequently used to model real-world systems. Thus, there exist extensions for Petri nets which allow to model times and priorities. In contrast, many proof techniques are based on classical (time-less and priority-less) Petri nets. However, this approach fails frequently for timed and prioritized Petri nets. In this paper, we present an approach to prove non-reachability in a Priority Duration Petri net. We use for this proving technique a state equation as well as conditions for firing that include a priority rule and a maximal step rule. Our approach leads to a system of equations and inequalities, which provide us with a sufficient condition of non-reachability. We demonstrate the application of our approach with an example
10
Content available remote Using State Equation to Prove Non-Reachability in Timed Petrinets
Popova-Zeugmann L., Werner M., Richling J.
Fundamenta Informaticae
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2003
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Vol. 55, nr 2
187-202
EN
Non-reachability proofs in Timed Petrinets were usually done by proving the non-reachability within the underlying timeless net. However, in many cases this approach fails. In this paper, we present an approach to prove non-reachability within the actual Timed Petrinet. For this purpose, we introduce a state equation for Timed Petrinets in analogy to timeless nets. Using this state equation, we can express reachability as a system of equations and inequations, which is solvable in polynomial time.
11
Content available remote Verification of Non-functional Properties of a Composable Architecture with Petrinets
Richling J., Popova-Zeugmann L., Werner M.
Fundamenta Informaticae
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2002
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Vol. 51, nr 1,2
185-200
EN
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 time-extended Petrinets. As a result, the first 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.
12
Content available remote Analyzing paths in Time Petri Nets
Popova-Zeugmann L., Schlatter D.
Fundamenta Informaticae
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1999
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Vol. 37, Nr 3
311-327
EN
In this paper, a parametric description of a transition sequence in a Time Petri net is introduced. The minimal and maximal time duration of a transition sequence are shown to be integers and furthermore the mni/max path passes only integer-states. A necessary condition for the reachability of an arbitrary state is given.
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