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53
On the decidability of temporal properties of probabilistic pushdown automata
 IN PROC. OF STACS’05
, 2005
"... We consider qualitative and quantitative modelchecking problems for probabilistic pushdown automata (pPDA) and various temporal logics. We prove that the qualitative and quantitative modelchecking problem for ωregular properties and pPDA is in 2EXPSPACE and 3EXPTIME, respectively. We also pro ..."
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Cited by 43 (12 self)
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We consider qualitative and quantitative modelchecking problems for probabilistic pushdown automata (pPDA) and various temporal logics. We prove that the qualitative and quantitative modelchecking problem for ωregular properties and pPDA is in 2EXPSPACE and 3EXPTIME, respectively. We also prove that modelchecking the qualitative fragment of the logic PECTL ∗ for pPDA is in 2EXPSPACE, and modelchecking the qualitative fragment of PCTL for pPDA is in EXPSPACE. Furthermore, modelchecking the qualitative fragment of PCTL is shown to be EXPTIMEhard even for stateless pPDA. Finally, we show that PCTL modelchecking is undecidable for pPDA, and PCTL + modelchecking is undecidable even for stateless pPDA.
Characterizing EF and EX tree logics
 In CONCUR 2004
"... We describe the expressive power of temporal branching time logics that use the modalities EX and EF. We give a forbidden pattern characterization of the tree languages definable in three logics: EX, EF and EX+EF. The properties in these characterizations can be verified in polynomial time when give ..."
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Cited by 28 (7 self)
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We describe the expressive power of temporal branching time logics that use the modalities EX and EF. We give a forbidden pattern characterization of the tree languages definable in three logics: EX, EF and EX+EF. The properties in these characterizations can be verified in polynomial time when given a minimal deterministic bottomup tree automaton. We consider the definability problem for logics over binary trees: given a regular tree language decide if it can be expressed by a formula of the logic in question. The main motivation for considering this problem is to understand the expressive power of tree logics. Although a very old question, definability has gained new relevance with the XML community’s burgeoning interest in tree models [8]. Indeed, numerous new formalisms for describing tree properties have been recently proposed.
Pushdown module checking
, 2005
"... Model checking is a useful method to verify automatically the correctness of a system with respect to a desired behavior, by checking whether a mathematical model of the system satisfies a formal specification of this behavior. Many systems of interest are open, in the sense that their behavior depe ..."
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Cited by 25 (18 self)
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Model checking is a useful method to verify automatically the correctness of a system with respect to a desired behavior, by checking whether a mathematical model of the system satisfies a formal specification of this behavior. Many systems of interest are open, in the sense that their behavior depends on the interaction with their environment. The model checking problem for finite– state open systems (called module checking) has been intensively studied in the literature. In this paper, we focus on open pushdown systems and we study the related model–checking problem (pushdown module checking, for short) with respect to properties expressed by CTL and CTL ∗ formulas. We show that pushdown module checking against CTL (resp., CTL ∗ ) is 2Exptimecomplete (resp., 3Exptimecomplete). Moreover, we prove that for a fixed CTL (resp., CTL ∗ ) formula, the problem is Exptimecomplete. 1
Pushdown Module Checking with Imperfect Information
, 2012
"... The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems ( ..."
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Cited by 23 (14 self)
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The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system’s control states and pushdown store content. We study the complexity of this problem with respect to the branchingtime temporal logics CTL, CTL ∗ and the propositional µcalculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information.
Verification of deployed artifact systems via data abstraction
 In Proc. of ICSOC
, 2011
"... Abstract. Artifact systems are a novel paradigm for specifying and implementing business processes described in terms of interacting modules called artifacts. Artifacts consist of data and lifecycle models, accounting for the relational structure of the artifact state and its possible evolutions ove ..."
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Cited by 15 (8 self)
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Abstract. Artifact systems are a novel paradigm for specifying and implementing business processes described in terms of interacting modules called artifacts. Artifacts consist of data and lifecycle models, accounting for the relational structure of the artifact state and its possible evolutions over time. We consider the problem of verifying artifact systems against specifications expressed in quantified temporal logic. This problem is in general undecidable. However, when artifact systems are deployed, their states can contain only a bounded number of elements. We exploit this fact to develop an abstraction technique that enables us to verify deployed artifact systems by model checking their bounded abstraction. 1
Reasoning about nondeterminism in programs
"... Branchingtime temporal logics (e.g. CTL, CTL ∗ , or the modal µcalculus) allow us to ask sophisticated questions about the nondeterminism that appears in systems. Applications of this type of reasoning include planning, games, security analysis, disproving, precondition synthesis, environment synt ..."
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Cited by 13 (5 self)
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Branchingtime temporal logics (e.g. CTL, CTL ∗ , or the modal µcalculus) allow us to ask sophisticated questions about the nondeterminism that appears in systems. Applications of this type of reasoning include planning, games, security analysis, disproving, precondition synthesis, environment synthesis, etc. Unfortunately, existing automatic branchingtime verification tools have limitions that have traditionally restricted their applicability (e.g. pushdown systems only, universal path quantifiers only, etc). In this paper we introduce an automation strategy that lifts many of these previous restrictions. Our method works reliably for properties with nontrivial mixtures of universal and existential modal operators. Furthermore, our approach supports (possibly infinitestate) programs. The basis of our approach is the observation that existential reasoning can be reduced to universal reasoning if the system’s statespace is appropriately restricted. This restriction on the statespace must meet a constraint derived from recent work on proving nontermination. The observation leads to a new route for implementation based on existing tools. To demonstrate the practical viability of our approach, we report on the results applying our preliminary implementation to a set of benchmarks drawn from the Windows operating system, the PostgreSQL database server, SoftUpdates patching system, as well as other handcrafted examples. 1.
On the computational complexity of verifying onecounter processes
 IN PROCEEDINGS OF THE 24TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS 2009
, 2008
"... Onecounter processes are pushdown systems over a singleton stack alphabet (plus a stackbottom symbol). We study the complexity of two closely related verification problems over onecounter processes: model checking with the temporal logic EF, where formulas are given as directed acyclic graphs, a ..."
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Cited by 12 (4 self)
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Onecounter processes are pushdown systems over a singleton stack alphabet (plus a stackbottom symbol). We study the complexity of two closely related verification problems over onecounter processes: model checking with the temporal logic EF, where formulas are given as directed acyclic graphs, and weak bisimilarity checking against finite systems. We show that both problems are P NPcomplete. This is achieved by establishing a close correspondence with the membership problem for a natural fragment of Presburger Arithmetic, which we show to be P NPcomplete. This fragment is also a suitable representation for the global versions of the problems. We also show that there already exists a fixed EF formula (resp. a fixed finite system) such that model checking (resp. weak bisimulation) over onecounter processes is hard for P NP[log]. However, the complexity drops to P if the onecounter process is fixed.
Verifying Probabilistic Procedural Programs
, 2004
"... Monolithic nitestate probabilistic programs have been abstractly modeled by nite Markov chains, and the algorithmic veri  cation problems for them have been investigated very extensively. In this paper we survey recent work conducted by the authors together with colleagues on the algorithmi ..."
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Cited by 12 (3 self)
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Monolithic nitestate probabilistic programs have been abstractly modeled by nite Markov chains, and the algorithmic veri  cation problems for them have been investigated very extensively. In this paper we survey recent work conducted by the authors together with colleagues on the algorithmic veri cation of probabilistic procedural programs ([BKS,EKM04,EY04]). Probabilistic procedural programs can more naturally be modeled by recursive Markov chains ([EY04]), or equivalently, probabilistic pushdown automata ([EKM04]). A very rich theory emerges for these models. While our recent work solves a number of veri cation problems for these models, many intriguing questions remain open.