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12
LTL with the freeze quantifier and register automata
 In LICS’06
, 2006
"... Temporal logics, firstorder logics, and automata over data words have recently attracted considerable attention. A data word is a word over a finite alphabet, together with a datum (an element of an infinite domain) at each position. Examples include timed words and XML documents. To refer to the d ..."
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Cited by 79 (7 self)
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Temporal logics, firstorder logics, and automata over data words have recently attracted considerable attention. A data word is a word over a finite alphabet, together with a datum (an element of an infinite domain) at each position. Examples include timed words and XML documents. To refer to the data, temporal logics are extended with the freeze quantifier, firstorder logics with predicates over the data domain, and automata with registers or pebbles. We investigate relative expressiveness and complexity of standard decision problems for LTL with the freeze quantifier (LTL ↓), 2variable firstorder logic (FO 2) over data words, and register automata. The only predicate available on data is equality. Previously undiscovered connections among those formalisms, and to counter automata with incrementing errors, enable us to answer several questions left open in recent literature. We show that the futuretime fragment of LTL ↓ which corresponds to FO 2 over finite data words can be extended considerably while preserving decidability, but at the expense of nonprimitive recursive complexity, and that most of further extensions are undecidable. We also prove that surprisingly, over infinite data words, LTL ↓ without the ‘until’ operator, as well as nonemptiness of oneway universal register automata, are undecidable even when there is only 1 register. 1.
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).
Temporal Logics on Words with Multiple Data Values
 In FSTTCS 2010
"... The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)pairs at each position. It considers a basic logic which is a semantical fragment of the logic LTL ↓ 1 of Demri and Lazic with operators for navigation into the future an ..."
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Cited by 10 (1 self)
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The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)pairs at each position. It considers a basic logic which is a semantical fragment of the logic LTL ↓ 1 of Demri and Lazic with operators for navigation into the future and the past. By reduction to the emptiness problem for data automata it is shown that this basic logic is decidable. Whereas the basic logic only allows navigation to positions where a fixed data value occurs, extensions are studied that also allow navigation to positions with different data values. Besides some undecidable results it is shown that the extension by a certain UNTILoperator with an inequality target condition remains decidable.
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
LTL over integer periodicity constraints (extended abstract
 In FOSSACS'04, Lecture Notes in Computer Science
, 2004
"... Abstract. Periodicity constraints are present in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. We introduce the logic PLTL mod, an extension of LinearTime Temporal Logic LTL with pasttime operators whose atom ..."
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Abstract. Periodicity constraints are present in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. 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. The underlying constraint language is a fragment of Presburger arithmetic shown to admit a pspacecomplete satisfiability problem and we establish that PLTL mod modelchecking and satisfiability problems are in pspace as plain LTL. The logic PLTL mod is a quite rich and concise language to express periodicity constraints. We show that adding logical quantification to PLTL mod provides expspacehard problems. As another application, we establish that the equivalence problem for extended singlestring automata, known to express the equality of time granularities, is pspacecomplete. The paper concludes by presenting a bunch of open problems related to fragments of Presburger LTL. 1
On the Equivalence of Automatonbased Representations of Time Granularities
"... A time granularity can be viewed as the partitioning of a temporal domain in groups of elements, where each group is perceived as an indivisible unit. In this paper we explore an automatonbased approach to the management of time granularity that compactly represents time granularities as singlestr ..."
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A time granularity can be viewed as the partitioning of a temporal domain in groups of elements, where each group is perceived as an indivisible unit. In this paper we explore an automatonbased approach to the management of time granularity that compactly represents time granularities as singlestring automata with counters, that is, Büchi automata, extended with counters, that accept a single infinite word. We focus our attention on the equivalence problem for the class of restricted labeled singlestring automata (RLA for short). The equivalence problem for RLA is the problem of establishing whether two given RLA represent the same time granularity. The main contribution of the paper is the reduction of the (non)equivalence problem for RLA to the satisfiability problem for linear diophantine equations with bounds on variables. Since the latter problem has been shown to be NPcomplete, we have that the RLA equivalence problem is in coNP. 1.
Impartial Anticipation in RuntimeVerification ⋆
"... Abstract. In this paper, a uniform approach for synthesizing monitors checking correctness properties specified in lineartime logics at runtime is provided. Therefore, a generic threevalued semantics is introduced reflecting the idea that prefixes of infinite computations are checked. Then a conce ..."
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Abstract. In this paper, a uniform approach for synthesizing monitors checking correctness properties specified in lineartime logics at runtime is provided. Therefore, a generic threevalued semantics is introduced reflecting the idea that prefixes of infinite computations are checked. Then a conceptual framework to synthesize monitors from a logical specification to check an execution incrementally is established, with special focus on resorting to the automatatheoretic approach. The merits of the presented framework are shown by providing monitor synthesis approaches for a variety of different logics such as LTL, the lineartime µcalculus, PLTL mod, S1S, and RLTL. 1
Verifying qualitative and quantitative properties with LTL
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A Theory of Ultimately Periodic
"... Languages and Automata with an Application to Time Granularity Abstract In this paper, we develop a theory of regular ωlanguages that consist of ultimately periodic words only and we provide it with an automatonbased characterization. The resulting class of automata, called Ultimately Periodic Aut ..."
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Languages and Automata with an Application to Time Granularity Abstract In this paper, we develop a theory of regular ωlanguages that consist of ultimately periodic words only and we provide it with an automatonbased characterization. The resulting class of automata, called Ultimately Periodic Automata (UPA), is a subclass of the class of Büchi automata and inherits some properties of automata over finite words (NFA). Taking advantage of the similarities among UPA, Büchi automata, and NFA, we devise efficient solutions to a number of basic problems for UPA, such as the inclusion, the equivalence, and the size optimization problems. The original motivation for developing a theory of ultimately periodic languages and automata was to represent and to reason about sets of time granularities in knowledgebased and database systems. In the last part of the paper, we show that UPA actually allow one to represent (possibly infinite) sets of granularities, instead of single ones, in a compact and suitable to algorithmic manipulation way. In particular, we describe an application of UPA to a concrete time granularity scenario taken from clinical medicine. A short preliminary version of this paper appeared in [4].
Automata for Branching and Layered Structures
"... The aim of the thesis is to exploit different classes of (sequential and tree) automata for modeling and reasoning on infinite complex systems. The leitmotif underlying the results provided in the thesis is that, once one identifies a finite set of properties to be tested, any infinite complex syst ..."
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The aim of the thesis is to exploit different classes of (sequential and tree) automata for modeling and reasoning on infinite complex systems. The leitmotif underlying the results provided in the thesis is that, once one identifies a finite set of properties to be tested, any infinite complex system can be often reduced to a simpler one, which satisfies the same properties and presents strong regularities (e.g., periodicity) in its structure. As a consequence, checking properties of such a system can be done by considering only a finite number of components. As for sequential automata, the most simple example is the notion of singlestring automata, which recognizes a single infinite word. Such a notion of automaton makes it possible to represent and reason on any infinite ultimately periodic word by means of a finite number of states and transitions. The notion can then be refined by introducing counters in order to compactly represent repeated occurrences of the same substring in an infinite word. Thus, algorithms working on such a kind of representation exploit suitable abstractions of the configuration space of the automaton (these abstractions must take into account