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Decidability Issues for Petri Nets  a survey
, 1994
"... : We survey 25 years of research on decidability issues for Petri nets. We collect results on the decidability of important properties, equivalence notions, and temporal logics. 1. Introduction Petri nets are one of the most popular formal models for the representation and analysis of parallel proc ..."
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Cited by 89 (5 self)
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: We survey 25 years of research on decidability issues for Petri nets. We collect results on the decidability of important properties, equivalence notions, and temporal logics. 1. Introduction Petri nets are one of the most popular formal models for the representation and analysis of parallel processes. They are due to C.A. Petri, who introduced them in his doctoral dissertation in 1962. Some years later, and independently from Petri's work, Karp and Miller introduced vector addition systems [47], a simple mathematical structure which they used to analyse the properties of "parallel program schemata', a model for parallel computation. In their seminal paper on parallel program schemata, Karp and Miller studied some decidability issues for vector addition systems, and the topic continued to be investigated by other researchers. When Petri's ideas reached the States around 1970, it was observed that Petri nets and vector addition systems were mathematically equivalent, even though thei...
Decidability issues for Petri nets
 Petri Nets Newsletter
, 1994
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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Cited by 19 (0 self)
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
Programmability of Chemical Reaction Networks
"... Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard c ..."
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Cited by 8 (2 self)
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Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and
The covering and boundedness problems for branching vector addition systems
 LIPICS LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS
, 2009
"... The covering and boundedness problems for branching vector addition systems are ..."
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Cited by 7 (2 self)
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The covering and boundedness problems for branching vector addition systems are
On the Complexity of the lineartime μCalculus for Petri Nets
, 1997
"... We study the complexity of modelchecking Petri Nets w.r.t. the propositional lineartime calculus. Esparza has shown in [5] that it is decidable, but the space complexity of his algorithm is exponential in the size of the system and double exponential in the size of the formula. In this paper we s ..."
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Cited by 7 (0 self)
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We study the complexity of modelchecking Petri Nets w.r.t. the propositional lineartime calculus. Esparza has shown in [5] that it is decidable, but the space complexity of his algorithm is exponential in the size of the system and double exponential in the size of the formula. In this paper we show that the complexity in the size of the formula can be reduced to polynomial space. We also prove that this is the best one can do. We also show that for the subclass of BPPs the problem has already the same complexity as for arbitrary nets. Furthermore we obtain the same results for the linear time temporal logic LTL, which is strictly less expressive than the lineartime calculus. 1 Introduction There is now a well established theory for automatic verification of finite state concurrent systems. Recently, the problem of extending this theory to infinite state systems has been addressed. There are mainly two different directions for the automatic verification of infinite state systems...
Networks of Relations
, 2005
"... Project, and my advisor Shuki Bruck for supporting me during my studies. I would also like to thank Shuki for being a good advisor and collaborator. I am grateful not only to Shuki but to all the people I have worked with, including Erik Winfree and David Soloveichik, in collaboration with whom the ..."
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Cited by 5 (2 self)
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Project, and my advisor Shuki Bruck for supporting me during my studies. I would also like to thank Shuki for being a good advisor and collaborator. I am grateful not only to Shuki but to all the people I have worked with, including Erik Winfree and David Soloveichik, in collaboration with whom the material in section 3.4.2 was produced. My family has supported my adventure of being a student, especially my wife Éva, my children András, Adam, and Emma, my mother Sarah, and my grandfather Howard, and to them I am very grateful. iv Relations are everywhere. In particular, we think and reason in terms of mathematical and English sentences that state relations. However, we teach our students much more about how to manipulate functions than about how to manipulate relations. Consider functions. We know how to combine functions to make new functions, how to evaluate functions efficiently, and how to think about compositions of functions. Especially in the area of boolean functions, we have become experts in the theory and art of designing combinations of functions to yield what we want, and this expertise has led to techniques that enable
Some Complexity Results for Rings of Petri Nets
"... We define a subclass of Petri nets called m \Gamma state n \Gamma cycle Petri nets, each of which can be thought of as a ring of n bounded (by m states) Petri nets using n potentially unbounded places as joins. Let Ring(n; l; m) be the class of m \Gamma state n \Gamma cycle Petri nets in which the l ..."
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We define a subclass of Petri nets called m \Gamma state n \Gamma cycle Petri nets, each of which can be thought of as a ring of n bounded (by m states) Petri nets using n potentially unbounded places as joins. Let Ring(n; l; m) be the class of m \Gamma state n \Gamma cycle Petri nets in which the largest integer mentioned can be represented in l bits (when the standard binary encoding scheme is used). As it turns out, both the reachability problem and the boundedness problem can be decided in O(n(l + log m)) nondeterministic space. Our results provide a slight improvement over previous results for the socalled cyclic communicating finite state machines. We also compare and contrast our results with that of V ASS(n; l; s), which represents the class of ndimensional sstate VASSs where the largest integer mentioned can be described in l bits. Keywords: Communicating finite state machine, complexity, boundedness, Petri net, reachability, vector addition system with states. 1. Introdu...
The Academic Life of Louis E. Rosier
, 1993
"... This document is a celebration of his life and his accomplishments. ..."