Complexity results for 1-safe nets

Cheng, Allan; Esparza, Javier; Palsberg, Jens

doi:10.1007/3-540-57529-4_66

Cited by 37 publications

(23 citation statements)

References 30 publications

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“…Liveness is one of the important properties of Petri nets and its analysis is difficult (see Cheng, Esparza, & Palsberg, 1995). So far, both necessary and sufficient conditions are proposed only for some subclasses of Petri nets.…”

Section: Resultsmentioning

confidence: 99%

Deciding the liveness for a subclass of weighted Petri nets based on structurally circular wait

Liu

Chen

2014

International Journal of Systems Science

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Weighted Petri nets as a kind of formal language are widely used to model and verify discrete event systems related to resource allocation like flexible manufacturing systems. System of Simple Sequential Processes with Multi-Resources (S 3 PMR, a subclass of weighted Petri nets and an important extension to the well-known System of Simple Sequential Processes with Resources, can model many discrete event systems in which (1) multiple processes may run in parallel and (2) each execution step of each process may use multiple units from multiple resource types. This paper gives a necessary and sufficient condition for the liveness of S 3 PMR. A new structural concept called Structurally Circular Wait (SCW) is proposed for S 3 PMR. Blocking Marking (BM) associated with an SCW is defined. It is proven that a marked S 3 PMR is live if and only if each SCW has no BM. We use an example of multi-processor system-on-chip to show that SCW and BM can precisely characterise the (partial) deadlocks for S 3 PMR. Simultaneously, two examples are used to show the advantages of SCW in preventing deadlocks of S 3 PMR. These results are significant for the further research on dealing with the deadlock problem.

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Section: Resultsmentioning

confidence: 99%

Deciding the liveness for a subclass of weighted Petri nets based on structurally circular wait

Liu

Chen

2014

International Journal of Systems Science

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“…The last requirement states that there are no dead transitions in the initial state M 0 . Generally speaking, for a complex WF-net it may be intractable to decide soundness [15]. In this paper we do not verify soundness of an evolved composite service, but preserve the one using a basic change operation set.…”

Section: Every Node X P T Is On a Path From I To O;mentioning

confidence: 99%

LiveMig: An Approach to Live Instance Migration in Composite Service Evolution

Zeng

Huai

Sun

et al. 2009

2009 IEEE International Conference on Web Services

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Composite service evolution is one of the most important challenges to deal with in the field of service composition. In particular, this paper presents, LiveMig, an approach to live migration of composite service instance, which is a critical step for online composite service evolution. In LiveMig, a set of change operations preserving soundness is first defined. Second, a live instance state migration algorithm is proposed to determine if the state migration is allowed or not, and to compute the exact state after the migration. Finally, the correctness of LiveMig is theoretically proved, and an extensive set of simulations are performed to show its feasibility and effectiveness.

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“…Therefore this is a behavioral property, i.e., it depends on the initial marking. As for many problems of this kind, deciding whether a Petri net is persistent is PSPACE hard [9]. A more restricted class of nets is that of the conflict-free Petri nets [24,13,26].…”

Section: )mentioning

confidence: 99%

“…In a persistent Petri net, there is no conflict in any reachable marking, but deciding persistence of a Petri net is PSPACE hard [9]. In a conflict-free Petri net [13,26] (CF net) conflicts are avoided by a structural constraint, therefore CF nets are persistent for any initial marking.…”

Section: Introductionmentioning

confidence: 99%

“…This implies that ∪ t∈T L • t ⊆ ∪ t∈T L t • , and then T L is an autonomous set. (Time complexity) The initialization requires no more than one visit to the net, and hence time O(|P R | + |T R | + |A R |); the ''while'' loop (lines [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] is executed at most |P| times, and each arc (x, y) with y ∈ x • (at lines 11, or 14) is considered at most once during the execution of the algorithm, just after that node x has been deleted from the live subnet (lines 10, or 13). Hence, the overall running time of the algorithm is O(|P R | + |T R | + |A R |).…”

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confidence: 99%

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Linear time analysis of properties of conflict-free and general Petri nets

Alimonti

Feuerstein

Laura

et al. 2011

Theoretical Computer Science

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We introduce the notion of a T-path within Petri nets, and propose to adopt the model of directed hypergraphs in order to determine properties of nets: in particular, we study the relationships between T-paths and firable sequences of transitions. Let us consider a Petri net P = < P, T, A, M-0 > and the set of places with a positive marking in M-0, i.e., P-0 = {p vertical bar M-0(p) > 0}. If we regard the net as a directed graph, the existence of a simple path from any place in P-0 to a transition t is, of course, a necessary condition for the potential firability of t. This is sufficient only if the net is a state machine, where vertical bar(center dot)t vertical bar = vertical bar t(center dot)vertical bar = 1 for all t epsilon T. In this paper we show that the existence of a T-path from any subset of P-0 to a transition t is a more restrictive condition and is, again, a necessary condition for the potential firability of t. But, in this case: (a) if P is a conflict-free Petri net, this is also a sufficient condition, (b) if P is a general Petri net, t is potentially firable by increasing the number of tokens in P-0. For conflict-free nets (CFPN) we consider the following problems: (a) determining the set of firable transitions, (b) determining the set of covetable places, (c) determining the set of live transitions, (d) deciding the boundedness of the net. For all these problems we provide algorithms requiring linear space and time, i.e., O(vertical bar p vertical bar + vertical bar T vertical bar + vertical bar A vertical bar), for a net P = < P, T, A. M-0 >. Previous results for this class of networks are given by Howell et al. (1987) [20], providing algorithms for solving problems in conflict-free nets in O(vertical bar p vertical bar x vertical bar T vertical bar ) time and space. Given a Petri net and a marking M, the well-known coverability problem consists in finding a reachable marking M` such that M` >= M; this problem is known to be EXPSPACE hard (Rackoff (1978) [33]). For general Petri nets we provide a partial answer to this problem. M is coverable by augmentation if it is coverable from an augmented marking m`(0); of the initial marking M-0: M`(0) >= M-0 and, for all p epsilon P, M`(0)(p) = 0 if M-0(p) = 0. We solve this problem in linear time. The algorithms for computing T-paths are incremental: it is possible to modify the network (adding new places, transitions, arcs, tokens), and update the set of potentially firable transitions and coverable places without recomputing them from scratch. This feature is meaningful when used during the interactive design of a system. (c) 2010 Elsevier B.V. All rights reserved

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Complexity results for 1-safe nets

Cited by 37 publications

References 30 publications

Deciding the liveness for a subclass of weighted Petri nets based on structurally circular wait

Deciding the liveness for a subclass of weighted Petri nets based on structurally circular wait

LiveMig: An Approach to Live Instance Migration in Composite Service Evolution

Linear time analysis of properties of conflict-free and general Petri nets

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