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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 90 (17 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 5 (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
A.: 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 deci ..."
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Cited by 2 (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.
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 2 (0 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
Bouziane's algorithm for the Petri net reachability problem is incorrect
, 2000
"... Proceedings of FOCS'98 contain a paper by Zakariae Bouziane, which aims at showing a new algorithm for the Petri net reachability problem. In this note, the idea of Bouziane's approach is explained, and its serious flaw is exposed. ..."
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Proceedings of FOCS'98 contain a paper by Zakariae Bouziane, which aims at showing a new algorithm for the Petri net reachability problem. In this note, the idea of Bouziane's approach is explained, and its serious flaw is exposed.
ERRATA TO THE POPL’09 PAPER “VERIFYING LIVENESS OF ASYNCHRONOUS PROGRAMS”
"... Abstract. An error was discovered by M.F. Atig in the coverability graph based decision procedure we defined in [2]. We thank him for bringing the error to our knowledge. We refer the interested reader to [1] for updated results about the verification of liveness properties for asynchronous programs ..."
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Abstract. An error was discovered by M.F. Atig in the coverability graph based decision procedure we defined in [2]. We thank him for bringing the error to our knowledge. We refer the interested reader to [1] for updated results about the verification of liveness properties for asynchronous programs. We show below at Fig. 1 and 2 that the coverability graph does not provide enough precision to determine the existence of fair infinite runs. main () { b:=false; while(NONDET) { post h1(); loc1 post h2(); loc2 h1() { b:=true; init loop exit h1 h2 d F 1 d F 2 bF dT d 2 T 1 bT h2() { if (b==true) post h2(); dloc Figure 1. An asynchronous program and its PN counterpart which has a fair infinite run init loop i exit d F 1 (d T 1) i−1 (d T 2) ω. 1 2 PIERRE GANTY, RUPAK MAJUMDAR, AND ANDREY RYBALCHENKO
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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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