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203
Compositional Model Checking
, 1999
"... We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approac ..."
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Cited by 2407 (62 self)
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We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approach is that local properties are often not preserved at the global level. We present a general framework for using additional interface processes to model the environment for a component. These interface processes are typically much simpler than the full environment of the component. By composing a component with its interface processes and then checking properties of this composition, we can guarantee that these properties will be preserved at the global level. We give two example compositional systems based on the logic CTL*.
Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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Cited by 1107 (16 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
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 202 (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.
Temporal Query Languages: a Survey
, 1995
"... We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We als ..."
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Cited by 108 (11 self)
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We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We also address the issue of incomplete temporal information. 1 Introduction A temporal database is a repository of temporal information. A temporal query language is any query language for temporal databases. In this paper we propose a formal notion of temporal database and use this notion in surveying a wide spectrum of temporal query languages. The need to store temporal information arises in many computer applications. Consider, for example, records of various kinds: financial [37], personnel, medical [98], or judicial. Also, monitoring data, e.g., in telecommunications network management [4] or process control, has often a temporal dimension. There has been a lot of research in temporal dat...
The declarative past and imperative future: Executable temporal logic for interactive systems
 In Proc. Temporal Logic in Specification, Altrincham, UK, LNCS 398
, 1987
"... We propose a new paradigm in executable logic, that of the declarative past and imperative future. A future statement of temporal logic can be understood in two ways: the declarative way, that of describing the future as a temporal extension; and the imperative way, that of making sure that the futu ..."
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Cited by 80 (6 self)
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We propose a new paradigm in executable logic, that of the declarative past and imperative future. A future statement of temporal logic can be understood in two ways: the declarative way, that of describing the future as a temporal extension; and the imperative way, that of making sure that the future will happen the way we want it. Since the future has not yet happened, we have a language which can be both declarative and imperative. We regard our theme as a natural meeting between the imperative and declarative paradigms. More specifically, we describe a temporal logic with Since, Until and fixed point operators. The logic is based on the natural numbers as the flow of time and can be used for the specification and control of process behaviour in time. A specification formula of this logic can be automatically rewritten into an executable form. In an executable form it can be used as a program for controlling process behaviour. The executable form has the structure "If A holds in the past then do B'. This structure shows that declarative and imperative programming can be integrated in a natural way.
Definability with Bounded Number of Bound Variables
 Information and Computation
, 1989
"... A theory satisfies the kvariable property if every firstorder formula is equivalent to a formula with at most k bound variables (possibly reused). Gabbay has shown that a model of temporal logic satisfies the kvariable property for some k if and only if there exists a finite basis for the tempora ..."
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Cited by 76 (5 self)
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A theory satisfies the kvariable property if every firstorder formula is equivalent to a formula with at most k bound variables (possibly reused). Gabbay has shown that a model of temporal logic satisfies the kvariable property for some k if and only if there exists a finite basis for the temporal connectives over that model. We give a modeltheoretic method for establishing the kvariable property, involving a restricted EhrenfeuchtFraisse game in which each player has only k pebbles. We use the method to unify and simplify results in the literature for linear orders. We also establish new kvariable properties for various theories of boundeddegree trees, and in each case obtain tight upper and lower bounds on k. This gives the first finite basis theorems for branchingtime models of temporal logic. 1 Introduction A firstorder theory \Sigma satisfies the kvariable property if every firstorder formula is equivalent under \Sigma to a formula with at most k bound variables (pos...
Efficient Checking of Temporal Integrity Constraints Using Bounded History Encoding
, 1995
"... : We present an efficient implementation method for temporal integrity constraints formulated in Past Temporal Logic. Although the constraints can refer to past states of the database, their checking does not require that the entire database history be stored. Instead, every database state is extend ..."
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Cited by 73 (6 self)
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: We present an efficient implementation method for temporal integrity constraints formulated in Past Temporal Logic. Although the constraints can refer to past states of the database, their checking does not require that the entire database history be stored. Instead, every database state is extended with auxiliary relations that contain the historical information necessary for checking constraints. Auxiliary relations can be implemented as materialized relational views. 1 Introduction Integrity constraints form an essential part of every database application. It is customary to distinguish between two kinds of constraints: static and temporal (or dynamic). Static constraints refer to the current state of the database, e.g.,"every manager is also an employee ", while temporal constraints may refer to past and future states in addition to the current state, e.g., "salaries of employees should never decrease" or "once a student drops out of the Ph.D. program, she should not be readmit...
On the Expressive Completeness of the Propositional MuCalculus With Respect to Monadic Second Order Logic
, 1996
"... . Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over tran ..."
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Cited by 65 (3 self)
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. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...
The Complexity of Firstorder and Monadic Secondorder Logic Revisited
 Annals of Pure and Applied Logic
, 2002
"... The modelchecking problem for a logic L on a class C of structures asks whether a given Lsentence holds in a given structure in C. In this paper, we give superexponential lower bounds for fixedparameter tractable modelchecking problems for firstorder and monadic secondorder logic. We show tha ..."
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Cited by 63 (6 self)
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The modelchecking problem for a logic L on a class C of structures asks whether a given Lsentence holds in a given structure in C. In this paper, we give superexponential lower bounds for fixedparameter tractable modelchecking problems for firstorder and monadic secondorder logic. We show that unless PTIME = NP, the modelchecking problem for monadic secondorder logic on finite words is not solvable in time f(k) · p(n), for any elementary function f and any polynomial p. Here k denotes the size of the input sentence and n the size of the input word. We prove the same result for firstorder logic under a stronger complexity theoretic assumption from parameterized complexity theory. Furthermore, we prove that the modelchecking problems for firstorder logic on structures of degree 2 and of bounded degree d ≥ 3 are not solvable in time 2 2o(k) · p(n) (for degree 2) and 2 22o(k) · p(n) (for degree d), for any polynomial p, again under an assumption from parameterized complexity theory. We match these lower bounds by corresponding upper bounds. 1.