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Dense Realtime Games
 IN LICS 02
, 2002
"... The rapid development of complex and safetycritical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to mode ..."
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Cited by 25 (4 self)
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The rapid development of complex and safetycritical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to model them is a twoplayer game: the system versus the environment. In this context, the central problem is to determine the existence of a winning strategy according to a given winning condition. We focus on realtime systems, and choose to model the related game as a nondeterministic timed automaton. We express winning conditions by formulas of the branchingtime temporal logic TCTL. While timed games have been studied in the literature, timed games with densetime winning conditions constitute a new research topic. The main result of this paper is an exponentialtime algorithm to check for the existence of a winning strategy for TCTL games where equality is not allowed in the timing constraints. Our approach consists on translating to timed tree automata both the game graph and the winning condition, thus reducing the considered decision problem to the emptiness problem for this class of automata. The proposed algorithm matches the known lower bound on timed games. Moreover, if we relax the limitation we have placed on the timing constraints, the problem becomes undecidable.
Automatatheoretic Decision of Timed Games
, 2013
"... The solution of games is a key decision problem in the context of verification of open systems and program synthesis. Given a game graph and a specification, we wish to determine if there exists a strategy of the protagonist that allows to select only behaviors fulfilling the specification. In this ..."
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Cited by 13 (3 self)
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The solution of games is a key decision problem in the context of verification of open systems and program synthesis. Given a game graph and a specification, we wish to determine if there exists a strategy of the protagonist that allows to select only behaviors fulfilling the specification. In this paper, we consider timed games, where the game graph is a timed automaton and the specification is given by formulas of the temporal logics Ltl and Ctl. We present an automatatheoretic approach to solve the addressed games, extending to the timed framework a successful approach to solve discrete games. The main idea of this approach is to translate the timed automaton A, modeling the game graph, into a tree automaton AT accepting all trees that correspond to a strategy of the protagonist. Then, given an automaton corresponding to the specification, we intersect it with the tree automaton AT and check for the nonemptiness of the resulting automaton. Our approach yields a decision algorithm running in exponential time for Ctl and in double exponential time for Ltl. The obtained algorithms are optimal in the sense that their computational complexity matches the known lower bounds.
Timed Tree Automata with an Application to Temporal Logic
 Acta Informatica
, 2001
"... Finite automata on !sequences and !trees were introduced in the sixties by Buchi, McNaughton and Rabin. Finite automata on timed !sequences were introduced by Alur and Dill. In this paper we extend the theory of timed !sequences to !trees. The main motivation is the introduction of a new way ..."
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Cited by 10 (5 self)
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Finite automata on !sequences and !trees were introduced in the sixties by Buchi, McNaughton and Rabin. Finite automata on timed !sequences were introduced by Alur and Dill. In this paper we extend the theory of timed !sequences to !trees. The main motivation is the introduction of a new way to specify realtime systems and to study, using automatatheoretic techniques, branchingtime temporal logics with timing constraints. We study closure properties and decision problems for the obtained classes of timed !tree languages. In particular, we show the decidability of the emptiness problem. As an application of the introduced theory, we give a new decidable branching time temporal logic (STCTL) whose semantics is based upon timed !trees. 1 Introduction Finite automata on !sequences and !trees were introduced in the sixties by Buchi [7], McNaughton [18] and Rabin [20]. Starting from these first works, a great amount of literature has been devoted to this theory which tur...
Finite Automata on Timed ωTrees
, 2001
"... In the last decade Alur and Dill introduced a model of automata on timed ωsequences which extends the traditional models of finite automata. In this paper we present a theory of timed ωtrees which extends both the theory of timed ωsequences and the theory of ωtrees. Main motivation is to intr ..."
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Cited by 1 (1 self)
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In the last decade Alur and Dill introduced a model of automata on timed ωsequences which extends the traditional models of finite automata. In this paper we present a theory of timed ωtrees which extends both the theory of timed ωsequences and the theory of ωtrees. Main motivation is to introduce a new way of specifying realtime systems and provide tools for studying decidability problems in related fields. We focus on the decision problems and their applications in system verification and synthesis.
Timed Information Flow Logic for Timed Automata
"... We study the problem of information ow in realtime systems described by Timed Automata. We distinguish between secret and observable actions of automata, we introduce a logic to express information ow properties as properties of the languages accepted by automata, and we give an algorithm to check ..."
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We study the problem of information ow in realtime systems described by Timed Automata. We distinguish between secret and observable actions of automata, we introduce a logic to express information ow properties as properties of the languages accepted by automata, and we give an algorithm to check these properties.
Timed Games With BranchingTime Winning Conditions
"... ... In this paper we focus on the verification of open realtime systems, modeled as nondeterministic timed automata [2]: finite automata augmented with a finite set of realvalued clocks. The transitions of a timed automaton are enabled according to the current state, that is, the current location ..."
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... In this paper we focus on the verification of open realtime systems, modeled as nondeterministic timed automata [2]: finite automata augmented with a finite set of realvalued clocks. The transitions of a timed automaton are enabled according to the current state, that is, the current location and the current clock values. In a transition, clocks can be instantaneously reset. The value of a clock is exactly the time elapsed since the last time it was reset. A clock constraint (guard) is associated to each transition with the meaning that a transition can be taken only if the associated guard is enabled. A clock constraint (invariant) can also be associated to each location with the meaning that the automaton can stay in a location as long as the corresponding invariant remains true. When
An AutomatonTheoretic Approach to Safety and Security in RealTime Systems
, 2003
"... Hybrid Systems are automata equipped with variables. Constraints on these variables are expressed by Mathematical Logics. Hybrid Systems are used for modeling embedded systems and time dependent processes. In these branches of study safety and security are among the main requirements that a system m ..."
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Hybrid Systems are automata equipped with variables. Constraints on these variables are expressed by Mathematical Logics. Hybrid Systems are used for modeling embedded systems and time dependent processes. In these branches of study safety and security are among the main requirements that a system must satisfy, hence the interest of ways to express and prove these properties. The aim of the thesis is to extend the classical classes of Hybrid Systems and to study safety and security properties of real life systems. For this purpose, we consider di#erent subclasses of High Order Mathematical Logics over real variables, integers variables, arrays with infinite elements and parameters. We recall four classes which are enclosed in First Order Mathematical Logics and for which the satisfiability problem of a formula is known to be decidable. We consider two new classes of High Order Mathematical Logics, where arrays can be quantified, and we prove decidability results of satisfiability.
A Model of Finite Automata on Timed ωTrees
, 2001
"... In the last decade Alur and Dill introduced a model of automata on timed ωsequences which extends the traditional models of finite automata. In this paper we present a theory of timed ωtrees which extends both the theory of timed ωsequences and the theory of ωtrees. Main motivation is to introdu ..."
Abstract
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In the last decade Alur and Dill introduced a model of automata on timed ωsequences which extends the traditional models of finite automata. In this paper we present a theory of timed ωtrees which extends both the theory of timed ωsequences and the theory of ωtrees. Main motivation is to introduce a new way of specifying realtime systems and provide tools for studying decidability problems in the field of quantitative temporal logics. We study properties and decision problems of the obtained classes of timed ωtree languages. Our main result is the decidability of the emptiness problem for all the classes of timed ωtree automata we consider.
found at the ENTCS Macro Home Page. Adequacy and Complete Axiomatization for Timed Modal Logic
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