Results 1  10
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14
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
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Cited by 107 (19 self)
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Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
On decidability of LTL model checking for process rewrite systems
 in: FSTTCS 2006, LNCS 4337 (2006
"... Abstract. We establish a decidability boundary of the model checking problem for infinitestate systems defined by Process Rewrite Systems (PRS) or weakly extended Process Rewrite Systems (wPRS), and properties described by basic fragments of actionbased Linear Temporal Logic (LTL). It is known tha ..."
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Cited by 9 (1 self)
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Abstract. We establish a decidability boundary of the model checking problem for infinitestate systems defined by Process Rewrite Systems (PRS) or weakly extended Process Rewrite Systems (wPRS), and properties described by basic fragments of actionbased Linear Temporal Logic (LTL). It is known that the problem for general LTL properties is decidable for Petri nets and for pushdown processes, while it is undecidable for PA processes. As our main result, we show that the problem is decidable for wPRS if we consider properties defined by formulae with only modalities strict eventually and strict always. Moreover, we show that the problem remains undecidable for PA processes even with respect to the LTL fragment with the only modality until or the fragment with modalities next and infinitely often. 1
Verifying liveness for asynchronous programs
 IN: POPL 2009: PROC. 36TH ACM SIGACTSIGPLAN SYMP. ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 2009
"... Asynchronous or “eventdriven” programming is a popular technique to efficiently and flexibly manage concurrent interactions. In these programs, the programmer can post tasks that get stored in a task buffer and get executed atomically by a nonpreemptive scheduler at a future point. We give a decis ..."
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Cited by 5 (1 self)
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Asynchronous or “eventdriven” programming is a popular technique to efficiently and flexibly manage concurrent interactions. In these programs, the programmer can post tasks that get stored in a task buffer and get executed atomically by a nonpreemptive scheduler at a future point. We give a decision procedure for the fair termination property of asynchronous programs. The fair termination problem asks, given an asynchronous program and a fairness condition on its executions, does the program always terminate on fair executions? The fairness assumptions rule out certain undesired bad behaviors, such as where the scheduler ignores a set of posted tasks forever, or where a nondeterministic branch is always chosen in one direction. Since every liveness property reduces to a fair termination property, our decision procedure extends to liveness properties of asynchronous programs. Our decision
Approximating Petri net reachability along contextfree traces
 In FSTTCS, volume 13 of LIPIcs
, 2011
"... ABSTRACT. We investigate the problem asking whether the intersection of a contextfree language (CFL) and a Petri net language (PNL) is empty. Our contribution to solve this longstanding problem which relates, for instance, to the reachability analysis of recursive programs over unbounded data doma ..."
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Cited by 3 (1 self)
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ABSTRACT. We investigate the problem asking whether the intersection of a contextfree language (CFL) and a Petri net language (PNL) is empty. Our contribution to solve this longstanding problem which relates, for instance, to the reachability analysis of recursive programs over unbounded data domain, is to identify a class of CFLs called the finiteindex CFLs for which the problem is decidable. The kindex approximation of a CFL can be obtained by discarding all the words that cannot be derived within a budget k on the number of occurrences of nonterminals. A finiteindex CFL is thus a CFL which coincides with its kindex approximation for some k. We decide whether the intersection of a finiteindex CFL and a PNL is empty by reducing it to the reachability problem of Petri nets with weak inhibitor arcs, a class of systems with infinitely many states for which reachability is known to be decidable. Conversely, we show that the reachability problem for a Petri net with weak inhibitor arcs reduces to the emptiness problem of a finiteindex CFL intersected with a PNL. 1
Integer Vector Addition Systems with States
"... Abstract. This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finitestate controller with a finite number of counters ranging over the integers. Although it is fo ..."
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Cited by 2 (2 self)
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Abstract. This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finitestate controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ZVASS is NPcomplete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an indepth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermannhardness of reachability and coverability, respectively, they can be added to ZVASS while retaining NPcompleteness of both coverability and reachability. 1
Reachability in Register Machines with Polynomial Updates
"... Abstract. This paper introduces a class of register machines whose registers can be updated by polynomial functions when a transition is taken, and the domain of the registers can be constrained by linear constraints. This model strictly generalises a variety of known formalisms such as various clas ..."
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Cited by 2 (1 self)
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Abstract. This paper introduces a class of register machines whose registers can be updated by polynomial functions when a transition is taken, and the domain of the registers can be constrained by linear constraints. This model strictly generalises a variety of known formalisms such as various classes of Vector Addition Systems with States. Our main result is that reachability in our class is PSPACEcomplete when restricted to one register. We moreover give a classification of the complexity of reachability according to the type of polynomials allowed and the geometry induced by the rangeconstraining formula. 1
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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Cited by 1 (0 self)
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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.
Static Provenance Verification for Message Passing Programs
"... Abstract. Provenance information records the source and ownership history of an object. We study the problem of provenance tracking in concurrent programs, in which several principals execute concurrent processes and exchange messages over unbounded but unordered channels. The provenance of a messa ..."
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Abstract. Provenance information records the source and ownership history of an object. We study the problem of provenance tracking in concurrent programs, in which several principals execute concurrent processes and exchange messages over unbounded but unordered channels. The provenance of a message, roughly, is a function of the sequence of principals that have transmitted the message in the past. The provenance verification problem is to statically decide, given a message passing program and a set of allowed provenances, whether the provenance of all messages in all possible program executions, belongs to the allowed set. We formalize the provenance verification problem abstractly in terms of wellstructured provenance domains, and show a general decidability result for it. In particular, we show that if the provenance of a message is a sequence of principals who have sent the message, and a provenance query asks if the provenance lies in a regular set, the problem is decidable and EXPSPACEcomplete. While the theoretical complexity is high, we show an implementation of our technique that performs efficiently on a set of Javascript examples tracking provenances in Firefox extensions. Our experiments show that many browser extensions store and transmit user information although the user sets the browser to the private mode. 1
Bouziane's algorithm for the Petri net reachability problem and incorrectness of the . . .
"... ..."
unknown title
, 1994
"... Linear logic, introduced by Girard, is a renement of classical logic with a natural, intrinsic accounting of resources. This accounting is made possible by removing the \structural " rules of contraction and weakening; adding a modal operator; and adding ner versions of the propositional connec ..."
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Linear logic, introduced by Girard, is a renement of classical logic with a natural, intrinsic accounting of resources. This accounting is made possible by removing the \structural " rules of contraction and weakening; adding a modal operator; and adding ner versions of the propositional connectives. Linear logic has fundamental logical interest and applications to computer science, particularly to Petri nets, concurrency, storage allocation, garbage collection, and the control structure of logic programs. In addition, there is a direct correspondence between polynomialtime computation and proof normalization in a bounded form of linear logic. In this paper we show that unlike most other propositional (quantierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for fragments of noncommutative