Esparza, J.: Decidability and complexity of Petri net problems - an introduction, in: Lectures on Petri Nets I: Basic Models. Advances in Petri Nets, vol. 1491 of Lecture Notes in Computer Science, Springer-Verlag, 1998, 374--428.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....The reader is referred to other texts (e.g. Rei88] for more comprehensive introductions to Petri Nets. 1 Safe Petri Nets model finite state systems, and are su#cient to represent all narrative structures in which we are interested (formal expressiveness results can be found, e.g. in [CEP95,Esp98] For instance, an expanded version of the simple lock puzzle, discussed in Section 1.2 is illustrated as a Petri Net in Figure 2. Transitions are drawn as small lines, places as circles and the marking by the presence absence of a black dot in each place. To unlock the door, the in computer ....

....(F, # ) # p Remarks: The parameter p defines how quickly one must reach the Lose state if the game is not winnable. A small value of p ensures a quick termination of a failed game. Verifying this property in general involves determining reachability, a wellconsidered problem in Petri Nets [Esp98] There are a variety of e#cient solutions available; e.g. PCP99] 4.2 Narrative Progress It is possible to build a simple semantics for a DAG based model by describing narrative progression as following a partial order on DAG subgraphs. A subgraph ordering, however, is too coarse for our ....

J. Esparza. Decidability and complexity of petri net problems---an introduction. In Lectures on Petri Nets I: Basic Models. Springer-Verlag, 1998.

....is deadlock detection. Definition 2 (Deadlock detection) Given a 1 safe P T net #, is there a reachable marking M which does not enable any transition of # Most analysis questions including deadlock detection and LTL model checking are PSPACE complete in the size of a 1 safe Petri net, see e.g. [9]. In bounded model checking we fix a bound n and look for counterexamples which are shorter than the given bound n. For example, in the case of bounded deadlock detection we look for executions reaching a deadlock in at most n transitions. It is easy to show that, e.g. the bounded deadlock ....

J. Esparza. Decidability and complexity of Petri net problems -- An introduction. In Lectures on Petri Nets I: Basic Models, volume 1491 of Lecture Notes in Computer Science, pages 374--428. Springer-Verlag, 1998.

....as a symbolic representation of all the processes of the 1 safe Petri net in question, which have a depth equal to a user specified value n. An extensive treatment of Petri net processes can be found in [4, 5] For computational complexity of Petri net related verification problems, see e.g. [18]. More information on the state explosion problem and methods to alleviate it can be found in [70] For a longer introduction to model checking, including other related techniques, see e.g. 11] Our research goal has been the development of efficient model checking methods for 1 safe Petri ....

....explicitly otherwise stated. It is well known that most verification problems for 1 safe Petri nets such as: reachability of a marking, existence of a reachable deadlock, LTL model checking, and CTL model checking are PSPACE complete in the size of the net system, for an introduction see e.g. [18]. Reachability with Prefixes. McMillan showed that deadlock checking using a finite complete prefix as input is NP complete in the size of the prefix [55] However, the prefix can sometimes be exponentially larger than the 1 safe Petri net from which it was created, thus explaining the difference ....

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J. Esparza. Decidability and complexity of Petri net problems -- An introduction. In Lectures on Petri Nets I: Basic Models, pages 374-- 428. Springer-Verlag, 1998. LNCS 1491.

....of the decidability proof (the first one was Kosaraju at STOC 82) nevertheless they did not improve the upper bound on the complexity, which thus remains nonprimitive recursive. On the other hand, the problem is known to be EXPSPACE hard due to Lipton [3] the proof can be also found, e.g. in [2]) Thus the complexity of the Petri net reachability problem remains unclear and it keeps to be an intellectual challenge to determine it. In the Proceedings FOCS 98 [1] Z. Bouziane claims to provide a primitive recursive (in fact, doubleexponential) algorithm. He first transforms the ....

Esparza J.: Decidability and Complexity of Petri Net Problems -- an Introduction. Lectures on Petri Nets I: Basic Models. Advances in Petri Nets. G. Rozenberg and W. Reisig (Eds.). Lecture Notes in Computer Science 1491, 374--428 (1998).

....questions concerning the behaviour of the system. The expressive power of CP nets inherited from Place Transition nets [24] and inscription languages such as the SML language [57] implies that essentially all interesting veri cation questions concerning CP nets are undecidable (for a survey see [29]) However, many CP nets arising in practice have a nite state space making veri cation possible. Unfortunately, state space methods su er from the so called state explosion problem: Even relatively small systems may have an astronomically number of reachable states [66] Development of ....

J. Esparza. Decidability and Complexity of Petri Net Problems - An Introduction. In Lecture on Petri Nets I: Basic Models, volume 1491 of Lecture Notes in Computer Science, pages 374-428. Springer-Verlag, 1998.

....stronger logic LT has been considered. As it turns out, the decidability of the model checking problem for LT and Petri nets is sensitive to whether atomic propositions beyond just true are allowed in the logic or not. As shown by Esparza, the case with general atomic propositions is undecidable [53], while in case that true is the only allowed atomic proposition this problem becomes decidable [51] The given decision procedure is based on an automata theoretic characterisation of the logic which was introduced by Vardi and Wolper [146] Refining a technique of [47] Esparza has shown that, ....

....space bounded universal Minsky n counter machine, for which, consequently, the acceptance problem is EXPSPACE hard. ffl Third, this universal Minsky n counter machine can be encoded as a parallel composition of a BPP and a finite automaton yielding a PPDA similar to the construction in [103] or [53]. The size of this finite automaton is a function in the size of the finite control of the universal counter machine and thus fixed and finite. ffl Fourth, the problem if the resulting PPDA has an infinite run can be encoded in a model checking problem for BPP and an LTL formula. The LTL formula ....

J. Esparza. Decidability and complexity of Petri net problems: An introduction. In W. Reisig and G. Rozenberg, editors, Lectures on Petri Nets I: Basic Models, LNCS 1491, pages 374--428. Springer, 1998.

....is deadlock detection. Definition 1. Deadlock) Given a 1 safe P T net #, is there a reachable marking M which does not enable any transition of # Most analysis questions including deadlock detection and LTL model checking are PSPACE complete in the size of a 1 safe Petri net, see e.g. [6]. In bounded model checking we fix a bound n and look for counterexamples which are shorter than the given bound n. For example, in the case of bounded deadlock detection in step semantics we look for step executions reaching a deadlock in n steps. It is easy to show that, e.g. the bounded ....

J. Esparza. Decidability and complexity of Petri net problems -- An introduction. In Lectures on Petri Nets I: Basic Models, pages 374--428. Springer-Verlag, 1998.

....n increases. See discussion in [3] on how to check whether a bound is su cient for completeness. Quite often a much smaller bound than the one discussed above su ces for completeness. For a general discussion of the computational complexity of veri cation problems for 1 safe Petri nets, see e.g. [6]. 2.2 Interleaving Semantics An interleaving execution is a step execution M 0 [S 0 #M 1 [S 1 # Mn 1 [S n 1 #Mn such that for all 0 # i # n 1 it holds that S i = 1. A marking is reachable in the interleaving semantics if there exists an interleaving execution # such that ....

J. Esparza. Decidability and complexity of Petri net problems  An introduction. In Lectures on Petri Nets I: Basic Models, pages 374428. Springer-Verlag, 1998. LNCS 1491.

.... Given a 1 safe P T net and a 1 safe marking M , is M a reachable marking of De nition 2 (Deadlock) Given a 1 safe P T net , is there a reachable marking M , which does not enable any transition of Both the reachability and deadlock problems for 1 safe Petri nets are PSPACEcomplete [12, 6]. In the bounded case there are now two problems and two di erent semantics to consider. We will de ne only one of them, the others are de ned in a similar fashion. De nition 3 (Bounded deadlock, step semantics) Given a 1 safe P T net and an integer bound n 0, is there a marking M reachable ....

J. Esparza. Decidability and complexity of Petri net problems{An introduction. In Lectures on Petri Nets I: Basic Models, pages 374-428. Springer-Verlag, 1998.

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Esparza, J.: Decidability and complexity of Petri net problems - an introduction, in: Lectures on Petri Nets I: Basic Models. Advances in Petri Nets, vol. 1491 of Lecture Notes in Computer Science, Springer-Verlag, 1998, 374--428.

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J. Esparza. Decidability and complexity of Petri net problems - an introduction. Lectures on Petri Nets I: Basic Models. Advances in Petri Nets, LNCS 1491, 374-428, 1998.

No context found.

J. Esparza. Decidability and complexity of Petri net problems - an introduction. Lectures on Petri Nets I: Basic Models. Advances in Petri Nets, LNCS 1491, 374-428, 1998.

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Esparza, J.: Decidability and complexity of Petri net problems-an introduction. In Rozenberg, G., Reisig, W., eds.: Lectures on Petri Nets I: Basic models. Springer Verlag (1998) 374--428 Published as LNCS 1491.

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J. Esparza. Decidability and complexity of Petri net problems - an introduction. In Lectures on Petri Nets I: Basic Models, pages 374--428. Springer-Verlag, 1998. LNCS 1491.

No context found.

J. Esparza. Decidability and complexity of Petri net problems-an introduction. In G. Rozenberg and W. Reisig, editors, Lectures on Petri Nets I: Basic models., pages 374--428. Springer Verlag, 1998. Published as LNCS 1491.

No context found.

J. Esparza. Decidability and complexity of petri net problems-an introduction. In G. Rozenberg and W. Reisig, editors, Lectures on Petri Nets I: Basic models., pages 374--428. Springer Verlag, 1998. Published as LNCS 1491.

No context found.

J. Esparza. Decidability and complexity of Petri net problems -- An introduction. In Lectures on Petri Nets I: Basic Models, pages 374--428. Springer-Verlag, 1998. LNCS 1491.

No context found.

Esparza, J.: Decidability and Complexity of Petri Net Problems --- an Introduction, Lectures on Petri Nets I: Basic Models (W. Reisig, G. Rozenberg, Eds.), Lecture Notes in Computer Science 1491, Springer-Verlag, 1998.

No context found.

J. Esparza. Decidability and complexity of Petri net problems -- an introduction. In Lectures on Petri Nets I: Basic Models, volume 1491 of LNCS, pages 374--428. Springer-Verlag, 1998.

No context found.

J. Esparza. Decidability and complexity of Petri net problems-an introduction. In G. Rozenberg and W. Reisig, editors, Lectures on Petri Nets I: Basic models., pages 374--428. Springer Verlag, 1998. Published as LNCS 1491.

No context found.

J. Esparza. Decidability and complexity of Petri net problems -- An introduction. In Lectures on Petri Nets I: Basic Models, pages 374--428. Springer-Verlag, 1998. LNCS 1491.

No context found.

Esparza, J.: Decidability and Complexity of Petri Net Problems --- an Introduction, Lectures on Petri Nets I: Basic Models (W. Reisig, G. Rozenberg, Eds.), Lecture Notes in Computer Science 1491, Springer-Verlag, 1998.

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Esparza, J.: Decidability and Complexity of Petri Net Problems -- An Introduction. In: Reisig, W., Rozenberg, G. (eds.): Lectures on Petri nets I: Basic Models. LNCS 1491. Berlin, Heidelberg, New York: Springer-Verlag, 1998, pp. 374--428

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J. Esparza. Decidability and Complexity of Petri nets problems  an introduction, pages 374428. 1998. in [22].

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J. Esparza. Decidability and complexity of Petri net problems - an introduction. Lectures on Petri nets I: Basic Models, 1998. Springer LNCS 1491, pp. 374-428.

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