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16
Decidability of reachability in vector addition systems (preliminary version
 In STOC
, 1982
"... A convincing proof of the decidability of reachability is presented. in vector addition systems No drastically new ideas beyond those in Sacerdote and Tenney, and Mayr are made use of. The complicated tree constructions in the earlier proofs are completely eliminated. I. ..."
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Cited by 124 (0 self)
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A convincing proof of the decidability of reachability is presented. in vector addition systems No drastically new ideas beyond those in Sacerdote and Tenney, and Mayr are made use of. The complicated tree constructions in the earlier proofs are completely eliminated. I.
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 120 (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...
Vector addition systems reachability problem (a simpler solution)
 TURING100
"... The reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known to be decidable by algorithms based on the classical KosarajuLambertMayrSacerdoteTenney decomposition (KLMST decomposition). Recently from this decomposition, we deduced t ..."
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Cited by 36 (7 self)
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The reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known to be decidable by algorithms based on the classical KosarajuLambertMayrSacerdoteTenney decomposition (KLMST decomposition). Recently from this decomposition, we deduced that a final configuration is not reachable from an initial one if and only if there exists a Presburger inductive invariant that contains the initial configuration but not the final one. Since we can decide if a Preburger formula denotes an inductive invariant, we deduce from this result that there exist checkable certificates of nonreachability in the Presburger arithmetic. In particular, there exists a simple algorithm for deciding the general VAS reachability problem based on two semialgorithms. A first one that tries to prove the reachability by enumerating finite sequences of actions and a second one that tries to prove the nonreachability by enumerating Presburger formulas. In another recent paper we provided the first proof of the VAS reachability problem that is not based on the KLMST decomposition. The proof is based on the notion of production relations that directly proves the existence of Presburger inductive invariants. In this paper we propose new intermediate results that dramatically simplify this last proof.
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 25 (6 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
Networks of Relations
, 2005
"... 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 ..."
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Cited by 8 (2 self)
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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
Vector addition system reversible reachability problem
 In CONCUR 2011  Concurrency Theory  22nd International Conference, CONCUR 2011
"... Vol. 9(1:05)2013, pp. 1–16 www.lmcsonline.org ..."
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REACHABILITY IN TWODIMENSIONAL VECTOR ADDITION SYSTEMS WITH STATES IS PSPACECOMPLETE
"... Abstract. Determining the complexity of the reachability problem for vector addition systems with states (VASS) is a longstanding open problem in computer science. Long known to be decidable, the problem to this day lacks any complexity upper bound whatsoever. In this paper, reachability for twodi ..."
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Abstract. Determining the complexity of the reachability problem for vector addition systems with states (VASS) is a longstanding open problem in computer science. Long known to be decidable, the problem to this day lacks any complexity upper bound whatsoever. In this paper, reachability for twodimensional VASS is shown PSPACEcomplete. This improves on a previously known doubly exponential time bound established by Howell, Rosier, Huynh and Yen in 1986. The coverability and boundedness problems are also noted to be PSPACEcomplete. In addition, some complexity results are given for the reachability problem in twodimensional VASS and in integer VASS when numbers are encoded in unary. 1.
Efficient FaultTolerant Infrastructure
, 2013
"... Cloud computing is playing a vital role for processing big data. The infrastructure is built on top of largescale clusters of commodity machines. It is very challenging to properly manage the hardware resources in order to utilize them effectively and to cope with the inevitable failures that will ..."
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Cloud computing is playing a vital role for processing big data. The infrastructure is built on top of largescale clusters of commodity machines. It is very challenging to properly manage the hardware resources in order to utilize them effectively and to cope with the inevitable failures that will arise with such a large collection of hardware. In this thesis, task assignment and checkpoint placement for cloud computing infrastructure are studied. As data locality is critical in determining the cost of running a task on a specific machine, how tasks are assigned to machines has a big impact on job completion time. An idealized abstract model is presented for a popular cloud computing platform called Hadoop. Although Hadoop task assignment (HTA) is NPhard, an algorithm is presented with only an additive approximation gap. Connection is established between the HTA problem and the minimum makespan scheduling problem under the restricted assignment model. A new competitive ratio bound for the online GREEDY algorithm is obtained. Checkpoints allow recovery of longrunning jobs from failures. Checkpoints themselves might fail. The effect of checkpoint failures on job completion time is investigated. The sum of task success probability and checkpoint reliability greatly affects job completion time. When possible checkpoint placements are constrained, retaining only the most recent Ω(log n) possible checkpoints has at most a constant factor penalty. When task failures follow the Poisson distribution, two symmetries for nonequidistant placements are proved and a first order approximation to optimum placement interval is generalized.