Results 1 
9 of
9
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. ..."
Abstract

Cited by 91 (0 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 89 (5 self)
 Add to MetaCart
: 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 ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
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
Acceleration For Presburger Petri Nets
, 2013
"... The reachability problem for Petri nets is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immedi ..."
Abstract
 Add to MetaCart
The reachability problem for Petri nets is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immediate. However, in this case, the computation of a Presburger formula denoting the reachability set is an open problem. Recently this problem got closed by proving that if the reachability set of a Petri net is definable in the Presburger arithmetic, then the Petri net is flatable, i.e. its reachability set can be obtained by runs labeled by words in a bounded language. As a direct consequence, classical algorithms based on acceleration techniques effectively compute a formula in the Presburger arithmetic denoting the reachability set.
On the Expressivity of Two Refinements of Multiplicative Exponential Linear Logic ⋆
, 2009
"... Abstract. The decidability of multiplicative exponential linear logic (MELL) is currently open. I show that two independently interesting refinements of MELL that alter only the syntax of proofs—leaving the underlying truth untouched— are undecidable. The first refinement uses new modal connectives ..."
Abstract
 Add to MetaCart
Abstract. The decidability of multiplicative exponential linear logic (MELL) is currently open. I show that two independently interesting refinements of MELL that alter only the syntax of proofs—leaving the underlying truth untouched— are undecidable. The first refinement uses new modal connectives between the linear and the unrestricted judgments, and the second is based on focusing with priority assignments that conforms to a staging discipline. Both refinements can adequately encode the transitions of a tworegister Minsky machine. While neither refinement is weak enough to entail the undecidability of MELL, they show that no additive connectives are necessary for undecidability. 1