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Realtime logics: complexity and expressiveness
 INFORMATION AND COMPUTATION
, 1993
"... The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via ..."
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Cited by 201 (16 self)
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The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by! regular sets. Several more expressive variants are proved to be highly undecidable. This framework allows us to classify a wide variety of realtime logics according to their complexity and expressiveness. Indeed, it follows that most formalisms proposed in the literature cannot be decided. We are, however, able to identify two elementary realtime temporal logics as expressively complete fragments of the theory of timed state sequences, and we present tableaubased decision procedures for checking validity. Consequently, these two formalisms are wellsuited for the speci cation and veri cation of realtime systems.
The Logical Modelling of Computational MultiAgent Systems
, 1992
"... THE aim of this thesis is to investigate logical formalisms for describing, reasoning about, specifying, and perhaps ultimately verifying the properties of systems composed of multiple intelligent computational agents. There are two obvious resources available for this task. The first is the (largel ..."
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Cited by 60 (17 self)
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THE aim of this thesis is to investigate logical formalisms for describing, reasoning about, specifying, and perhaps ultimately verifying the properties of systems composed of multiple intelligent computational agents. There are two obvious resources available for this task. The first is the (largely AI) tradition of reasoning about the intentional notions (belief, desire, etc.). The second is the (mainstream computer science) tradition of temporal logics for reasoning about reactive systems. Unfortunately, neither resource is ideally suited to the task: most intentional logics have little to say on the subject of agent architecture, and tend to assume that agents are perfect reasoners, whereas models of concurrent systems from mainstream computer science typically deal with the execution of individual program instructions. This thesis proposes a solution which draws upon both resources. It defines a model of agents and multiagent systems, and then defines two execution models, which ...
Dynamic Linear Time Temporal Logic
 IN ANNALS OF PURE AND APPLIED LOGIC
, 1997
"... A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S ..."
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Cited by 42 (3 self)
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A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S1S, the monadic secondorder theory of !sequences. In fact a sublogic of DLTL which corresponds to propositional dynamic logic with a linear time semantics is already as expressive as S1S. We pin down in an obvious manner the sublogic of DLTL which correponds to the first order fragment of S1S. We show that DLTL has an exponential time decision procedure. We also obtain an axiomatization of DLTL. Finally, we point to some natural extensions of the approach presented here for bringing together propositional dynamic and temporal logics in a linear time setting.
The Regular RealTime Languages
 In Proc. 25th Int. Coll. Automata, Languages, and Programming (ICALP'98
, 1998
"... . A specification formalism for reactive systems defines a class of !languages. We call a specification formalism fully decidable if it is constructively closed under boolean operations and has a decidable satisfiability (nonemptiness) problem. There are two important, robust classes of !languages ..."
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Cited by 35 (3 self)
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. A specification formalism for reactive systems defines a class of !languages. We call a specification formalism fully decidable if it is constructively closed under boolean operations and has a decidable satisfiability (nonemptiness) problem. There are two important, robust classes of !languages that are definable by fully decidable formalisms. The !regular languages are definable by finite automata, or equivalently, by the Sequential Calculus. The counterfree !regular languages are definable by temporal logic, or equivalently, by the firstorder fragment of the Sequential Calculus. The gap between both classes can be closed by finite counting (using automata connectives), or equivalently, by projection (existential secondorder quantification over letters). A specification formalism for realtime systems defines a class of timed !languages, whose letters have realnumbered time stamps. Two popular ways of specifying timing constraints rely on the use of clocks, and on the use...
An executable temporal logic to express safety properties and its connection with the language Lustre
 Universit’e Laval
, 1993
"... This paper studies the expressive power of the synchronous dataflow language Lustre as a specification language, and its connection with temporal logic. After a brief overview of Lustre, we define a temporal logic, called SL, which is shown to have exactly the expressive power of regular safety p ..."
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Cited by 10 (0 self)
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This paper studies the expressive power of the synchronous dataflow language Lustre as a specification language, and its connection with temporal logic. After a brief overview of Lustre, we define a temporal logic, called SL, which is shown to have exactly the expressive power of regular safety properties. Directly inspired from Boolean Lustre, this logic is executable, in the sense that the accepting automaton of any SL formula can be constructed "on the fly", as the model is read. Then we consider a fragment of SL, called DSL, for the formulas of which the accepting automaton built by the previous technique is deterministic. DSL is shown to have the same expressive power as SL, and to be equivalent to Boolean Lustre. 1 Introduction Lustre [CPHP87, HCRP91] is a synchronous declarative language designed for programming realtime systems. It is based on the dataflow principle [Kah74, AW85], with a strong restriction which consists in considering that all the variables involved in ...
Tool support for learning Büchi automata and linear temporal logic
 Presented at the Formal Methods in the Teaching Lab Workshop
, 2006
"... Abstract. Automata and logics are intimately related, and understanding their relation is instrumental in discovering algorithmic solutions to formal reasoning problems or simply in using those solutions. This applies to Büchi automata and linear temporal logic, which have become fundamental compone ..."
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Cited by 2 (1 self)
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Abstract. Automata and logics are intimately related, and understanding their relation is instrumental in discovering algorithmic solutions to formal reasoning problems or simply in using those solutions. This applies to Büchi automata and linear temporal logic, which have become fundamental components of the modelchecking approach to formal verification of concurrent systems. Translation of a propositional temporal formula into an equivalent Büchi automaton is routinely performed in many modelchecking algorithms and tools. Albeit the possibility of mechanical translation, a temporal formula and its equivalent automaton appear to be two very different artifacts and their correspondence is not easy to grasp. In this paper, we introduce a graphical interactive tool, named GOAL, that can assist the user in understanding the relation between Büchi automata and linear temporal logic, and suggest possible usages and benefits of the tool in courses where modelchecking techniques are covered. GOAL builds on the successful JFLAP tool for classic theory of automata and formal languages. One main function of GOAL is translation of a propositional temporal formula into an equivalent Büchi automaton that can be visually manipulated, for example, running the automaton on some input. GOAL also supports various standard operations and tests, including equivalence test, on Büchi automata. We believe that, with an easy access to temporal formulae and their graphically presented equivalent Büchi automata, the student’s understanding of the two formalisms and their relation will be greatly enhanced. 1
Quantified CTL: expressiveness and complexity
 Research Report LSV1307, Lab. Spécification & Vérification, ENS
, 2013
"... Abstract. While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its ex ..."
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Cited by 1 (1 self)
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Abstract. While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its expressiveness (showing in particular that QCTL coincides with Monadic SecondOrder Logic for both semantics) and characterise the complexity of its modelchecking and satisfiability problems, depending on the number of nested propositional quantifiers (showing that the structure semantics populates the polynomial hierarchy while the tree semantics populates the exponential hierarchy). Temporal logics. 1.
Membres du Jury:
"... présentée à l’Université d’Orléans pour obtenir le grade de Docteur de l’Université d’Orléans par: ..."
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présentée à l’Université d’Orléans pour obtenir le grade de Docteur de l’Université d’Orléans par:
Quantified CTL: expressiveness and model checking (Extended abstract)
"... Abstract. While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its ex ..."
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Abstract. While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its expressiveness (showing in particular that QCTL coincides with Monadic SecondOrder Logic for both semantics) and characterize the complexity of its modelchecking problem, depending on the number of nested propositional quantifiers (showing that the structure semantics populates the polynomial hierarchy while the tree semantics populates the exponential hierarchy). We also show how these results apply to model checking ATLlike temporal logics for games. 1