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31
On the freeze quantifier in constraint LTL: decidability and complexity
 I & C
, 2005
"... Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some realtime logics, but this variablebinding mechanism is quite general ..."
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Cited by 28 (8 self)
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Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some realtime logics, but this variablebinding mechanism is quite general and ubiquitous in many logical languages (firstorder temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, etc.). We show that Constraint LTL over the simple domain =# augmented with the freeze operator is undecidable which is a surprising result regarding the poor language for constraints (only equality tests). Many versions of freezefree Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes # 1 completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACEcompleteness) or when the formulae are flat in a sense introduced in the paper. Our undecidability results are quite sharp (i.e. with restrictions on the number of variables) and all our complexity characterizations insure completeness with respect to some complexity class (mainly PSPACE and EXPSPACE).
Combining Spatial and Temporal Logics: Expressiveness Vs. Complexity
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2004
"... In this paper, we construct and investigate a hierarchy of spatiotemporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic the spatial logics RCC8, BRCC8, S4 u and their fragments. The obtained results give ..."
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Cited by 25 (9 self)
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In this paper, we construct and investigate a hierarchy of spatiotemporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic the spatial logics RCC8, BRCC8, S4 u and their fragments. The obtained results give a clear picture of the tradeoff between expressiveness and `computational realisability' within the hierarchy. We demonstrate how di#erent combining principles as well as spatial and temporal primitives can produce NP, PSPACE, EXPSPACE, 2EXPSPACEcomplete, and even undecidable spatiotemporal logics out of components that are at most NP or PSPACEcomplete.
On the Computational Complexity of SpatioTemporal Logics
 Proceedings of the 16th AAAI International FLAIRS Conference
, 2003
"... Recently, a hierarchy of spatiotemporal languages based on the propositional temporal logic PTL and the spatial languages RCC8, BRCC8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open. ..."
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Cited by 21 (0 self)
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Recently, a hierarchy of spatiotemporal languages based on the propositional temporal logic PTL and the spatial languages RCC8, BRCC8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open.
Algebraic recognizability of languages
 In Proc. 29th Int. Symp. Math. Found. of Comp. Sci. (MFCS’04
, 2004
"... Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those ..."
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Cited by 13 (2 self)
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Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. In the beginning was the Word... Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. The notion of recognizable languages is a familiar one, associated with classical theorems by Kleene, Myhill, Nerode, Elgot, Büchi, Schützenberger, etc. It can be approached from several angles: recognizability by automata, recognizability by finite monoids or finiteindex congruences, rational expressions, monadic second
SMTbased Verification of LTL Specifications with Integer Constraints and its Applications to Runtime Checking of Service Substitutability
, 2010
"... Abstract—An important problem that arises during the execution of servicebased applications concerns the ability to determine whether a running service can be substituted with one with a different interface, for example if the former is no longer available. Standard Bounded Model Checking technique ..."
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Cited by 12 (3 self)
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Abstract—An important problem that arises during the execution of servicebased applications concerns the ability to determine whether a running service can be substituted with one with a different interface, for example if the former is no longer available. Standard Bounded Model Checking techniques can be used to perform this check, but they must be able to provide answers very quickly, lest the check hampers the operativeness of the application, instead of aiding it. The problem becomes even more complex when conversational services are considered, i.e., services that expose operations that have Input/Output data dependencies among them. In this paper we introduce a formal verification technique for an extension of Linear Temporal Logic that allows users to include in formulae constraints on integer variables. This technique applied to the substitutability problem for conversational services is shown to be considerably faster and with smaller memory footprint than existing ones.
LTL over integer periodicity constraints
 Proceedings of the 7th International Conference on Foundations of Software Science and Computation Structures (FOSSACS), volume 2987 of LNCS
, 2004
"... Abstract. Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of LinearTime Temporal Logic LTL with pasttime operators ..."
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Abstract. Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of LinearTime Temporal Logic LTL with pasttime operators whose atomic formulae are defined from a firstorder constraint language dealing with periodicity. Although the underlying constraint language is a fragment of Presburger arithmetic shown to admit a pspacecomplete satisfiability problem, we establish that PLTL mod modelchecking and satisfiability problems remain in pspace as plain LTL (full Presburger LTL is known to be highly undecidable). This is particularly interesting for dealing with periodicity constraints since the language of PLTL mod has a language more concise than existing languages and the temporalization of our firstorder language of periodicity constraints has the same worst case complexity as the underlying constraint language. Finally, we show examples of introduction the quantification in the logical language that provide to PLTL mod, expspacecomplete problems. As another application, we establish that the equivalence problem for extended singlestring automata, known to express the equality of time granularities, is pspacecomplete by designing a reduction from QBF and by using our results for PLTL mod. Keywords: Presburger LTL, periodicity constraints, computational complexity, Büchi automaton, QBF.
S.: Verification of gaporder constraint abstractions of counter systems
"... Abstract. We investigate verification problems for gaporder constraint systems (GCS), an (infinitelybranching) abstract model of counter machines, in which constraints (over Z) between the variables of the source state and the target state of a transition are gaporder constraints (GC) [27].GCS ex ..."
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Abstract. We investigate verification problems for gaporder constraint systems (GCS), an (infinitelybranching) abstract model of counter machines, in which constraints (over Z) between the variables of the source state and the target state of a transition are gaporder constraints (GC) [27].GCS extend monotonicity constraint systems [5], integral relation automata [12], and constraint automata in [15]. First, we show that checking the existence of infinite runs in GCS satisfying acceptance conditions àlaBüchi (fairness problem) is decidable and PSPACEcomplete. Next, we consider a constrained branchingtime logic, GCCTL ∗ , obtained by enriching CTL ∗ with GC, thus enabling expressive properties and subsuming the setting of [12]. We establish that, while modelchecking GCS against the universal fragment of GCCTL ∗ is undecidable, modelchecking against the existential fragment, and satisfiability of both the universal and existential fragments are instead decidable and PSPACEcomplete (note that the two fragments are not dual since GC are not closed under negation). Moreover, our results imply PSPACEcompleteness of the verification problems investigated and shown to be decidable in [12], but for which no elementary upper bounds are known. 1
Bounded Reachability for Temporal Logic over Constraint System
 In Proc. TIME
, 2010
"... Many extensions of Propositional Linear Temporal Logic (PLTL) are proposed with the goal of verifying infinitestate systems whose formulae may include arithmetic constraints belonging to a specific constraint system [3, 6]. Among these, CLTL (Counter LTL) extends Propositional LTL with fu ..."
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Cited by 7 (4 self)
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Many extensions of Propositional Linear Temporal Logic (PLTL) are proposed with the goal of verifying infinitestate systems whose formulae may include arithmetic constraints belonging to a specific constraint system [3, 6]. Among these, CLTL (Counter LTL) extends Propositional LTL with fu
Branchingtime Temporal Logic Extended with Qualitative Presburger Constraints
"... Abstract. Recently, LTL extended with atomic formulas built over a constraint language interpreting variables in Z has been shown to have a decidable satisfiability and modelchecking problem. This language allows to compare the variables at different states of the model and include periodicity cons ..."
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Cited by 5 (2 self)
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Abstract. Recently, LTL extended with atomic formulas built over a constraint language interpreting variables in Z has been shown to have a decidable satisfiability and modelchecking problem. This language allows to compare the variables at different states of the model and include periodicity constraints, comparison constraints, and a restricted form of quantification. On the other hand, the CTL counterpart of this logic (and hence also its CTL ∗ counterpart which subsumes both LTL and CTL) has an undecidable modelchecking problem. In this paper, we substantially extend the decidability border, by considering a meaningful fragment of CTL ∗ extended with such constraints (which subsumes both the universal and existential fragments, as well as the EFlike fragment) and show that satisfiability and modelchecking over relational automata that are abstraction of counter machines are decidable. The correctness and the termination of our algorithm rely on a suitable well quasiordering defined over the set of variable valuations. 1
Verification of qualitative Z constraints
"... Abstract. We introduce an LTLlike logic with atomic formulae built over a constraint language interpreting variables in Z. The constraint language includes periodicity constraints, comparison constraints of the form x = y and x < y, it is closed under Boolean operations and it admits a restricte ..."
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Abstract. We introduce an LTLlike logic with atomic formulae built over a constraint language interpreting variables in Z. The constraint language includes periodicity constraints, comparison constraints of the form x = y and x < y, it is closed under Boolean operations and it admits a restricted form of existential quantification. This is the largest set of qualitative constraints over Z known so far, shown to admit a decidable LTL extension. Such constraints are those used for instance in calendar formalisms or in abstractions of counter automata by using congruences modulo some power of two. Indeed, various programming languages perform arithmetic operators modulo some integer. We show that the satisfiability and modelchecking problems (with respect to an appropriate class of constraint automata) for this logic are decidable in polynomial space improving significantly known results about its strict fragments. As a byproduct, LTL modelchecking over integral relational automata is proved complete for polynomial space which contrasts with the known undecidability of its CTL counterpart. 1