Model Checking with Finite Complete Prefixes Is PSPACE-Complete

Heljanko, Keijo

doi:10.1007/3-540-44618-4_10

Cited by 7 publications

(4 citation statements)

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“…The finiteness is commonly achieved by identifying a set of cut-off events beyond which the unfolding is not generated. There have been some methods/algorithms to generate such a prefix that satisfies the above two requirements [7], [22]- [24], [29]. In order to utilize the unfolding technique to verify the soundness for WF-nets, we must generate a finite prefix.…”

Section: Basic Unfoldingmentioning

confidence: 99%

A Branching-Process-Based Method to Check Soundness of Workflow Systems

et al. 2016

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Workflow nets (WF-nets) as a class of Petri nets are widely used to model and analyze workflow systems. Soundness is an important property of WF-nets, which guarantees that the systems are deadlockand livelock-free and each task has a chance to be performed. Van der Aalst has proven that the soundness problem is decidable for WF-nets and we have also shown that it is PSPACE-complete for bounded ones. Since the definition of soundness is based on reachability and Van der Aalst has proven that a sound WF-net must be bounded, the soundness detection can be carried out via the reachability graph analysis. However, the state explosion problem is a big obstacle to this technique. The unfolding technique of Petri nets can effectively avoid/alleviate this problem. This paper proposes an algorithm to generate a finite prefix of the unfolding of a WF-net, called basic unfolding. Furthermore, a necessary and sufficient condition is proposed to decide soundness based on basic unfolding. In addition, some examples illustrate that the unfolding technique can save the storage space effectively.INDEX TERMS Petri nets, soundness, branching processes, unfolding, business process model.GUANJUN LIU (M'16) received the Ph.D. degree in computer software and theory from

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Section: Basic Unfoldingmentioning

confidence: 99%

A Branching-Process-Based Method to Check Soundness of Workflow Systems

et al. 2016

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“…Examples from planning include: the basic planning problem, that is, the problem of deciding whether a given instance of the propositional STRIPS planning problem has a solution, i.e., a plan, which was proven to be PSPACE-complete [4]; a whole range of planning problems in probabilistic planning domains [15]; planning problems in the presence of incompleteness [2]; and planning problems with temporal goals [3] (the reader is also referred to the survey paper [5]). Examples from model checking and Petri nets include: the problem of model checking with respect to Kripke structures and linear temporal logic, LTL, which was proven to be PSPACE-complete [17]; and the problems of model checking with respect to 1-safe Petri nets and both LTL and computation tree logic, CTL, which was proven to be PSPACE-complete [13] (the reader is referred to the survey papers [9] and [10]).…”

Section: Introductionmentioning

confidence: 99%

The complexity of achievement and maintenance problems in agent-based systems

Stewart

2003

Artificial Intelligence

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We completely classify the computational complexity of the basic achievement and maintenance agent design problems in bounded environments when these problems are parameterized by the number of environment states and the number of agent actions. The different problems are P-complete, NP-complete, co-NP-complete or PSPACE-complete (when they are not trivial). We also consider alternative achievement and maintenance agent design problems by allowing longer runs in environments (that is, our environments are bounded but the bounds are more liberal than was the case previously). Again, we obtain a complete classification but so that the different problems are DEXPTIME-complete, NEXPTIMEcomplete, co-NEXPTIME-complete or NEXPSPACE-complete (when they are not trivial).

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“…Both problems were overcome in the next years. Improved algorithms for constructing complete prefixes were described in [49,22,23,31,32,35,36,38,24], and extensions to (almost) arbitrary properties expressible in Linear Temporal Logic (LTL) were presented in [16,19,20].Since 2000 the algorithms for constructing complete prefixes have been parallelized [33,55] and distributed [5]. Initially developed for systems modeled as "plain" Petri nets, the unfolding approach has been extended to high-level Petri nets [37,55] [3,2].…”

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confidence: 99%

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A False History of True Concurrency: From Petri to Tools

Esparza

2010

Lecture Notes in Computer Science

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Abstract. I briefly review the history of the unfolding approach to model checking.Carl Adam Petri passed away on July 2, 2010. I learnt about his death three days later, a few hours after finishing this text. He was a very profound and highly original thinker, and will be sadly missed. This note is dedicated to his memory.In some papers and talks, Moshe Vardi has described the history of the automatatheoretic approach to model checking, the verification technique that inspired the SPIN model checker and other tools. He traces it back to the work of theoreticians like Büchi, Prior, Trakhtenbrot and others, whose motivations were surprisingly far away from the applications that their ideas found down the line. Inspired by this work, in this note I briefly present the origins of the unfolding approach to model checking [21], a branch of the automata-theoretic approach that alleviates the state-explosion problem caused by concurrency.Since the unfolding approach is based on the theory of true concurrency, describing its origins requires to speak about the origin of true concurrency itself. However, here I only touch upon those aspects of the theory that directly inspired the unfolding approach. This leaves many important works out, and so this is a very partial and "false" history of true concurrency.The theory of true concurrency starts with two fundamental contributions by Carl Adam Petri, described in detail by Brauer and Reisig in an excellent article [11]. Both were a result of Petri's interest in analyzing the connection between mathematical, abstract computing machines, and their physical realizations. In his dissertation "Kommunikation mit Automaten", defended in 1962, Petri observes that the performance of a physically implemented Turing machine will degrade over time if the machine uses more and more storage space, because in this case signals have to travel longer and longer distances over longer and longer wires. To solve this problem he proposes an asynchronous architecture in which the storage space can be extended while the machine continues to operate. In the dissertation this abstract machine is described with the help of several semi-formal representations, but three years later Petri has already distilled the first mathematical formalism for asynchronous computation, and, arguably, the beginning of concurrency theory: Petri nets.Petri's second contribution is an analysis of the notion of execution of a machine as a sequence of global states, or as a sequence of events ordered by their occurrence times with respect to some global clock. He observes that global states or global clocks are again a mathematical construct that cannot be "implemented": since information can only travel at finite speed, no part of a system can know the state of all its components at a certain moment in time.1 He proposes to replace executions by nonsequential processes, sets of events ordered not by the time at which they occur, but by the causality relation, which is independent of the observer. The theory of nonsequen...

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Model Checking with Finite Complete Prefixes Is PSPACE-Complete

Cited by 7 publications

References 18 publications

A Branching-Process-Based Method to Check Soundness of Workflow Systems

A Branching-Process-Based Method to Check Soundness of Workflow Systems

The complexity of achievement and maintenance problems in agent-based systems

A False History of True Concurrency: From Petri to Tools

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