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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 1300 (17 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
A Logic for Reasoning about Time and Reliability
 Formal Aspects of Computing
, 1994
"... We present a logic for stating properties such as, "after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are inter ..."
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Cited by 360 (1 self)
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We present a logic for stating properties such as, "after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satisfies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and This research report is a revised and extended version of a paper that has appeared under the title "A Framework for Reasoning about Time and Reliability" in the Proceeding of the 10 th IEEE Realtime Systems Symposium, Santa Monica CA, December 1989. This work was partially supported by the Swedish Board for Technical Development (STU) as part of Esprit BRA Project SPEC, and by the Swedish Telecommunication Administration. the Markov chain. A simple example is inc...
Automated Temporal Reasoning about Reactive Systems
, 1996
"... . There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective a ..."
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Cited by 41 (2 self)
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. There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective and reliable means of specifying and ensuring correct behavior of such systems. This paper discusses known complexity and expressiveness results for a number of such logics in common use and describes key technical tools for obtaining essentially optimal mechanical reasoning algorithms. However, the emphasis is on underlying intuitions and broad themes rather than technical intricacies. 1 Introduction There is a growing need for reliable methods of designing correct reactive systems. These systems are characterized by ongoing, typically nonterminating and highly nondeterministic behavior. Examples include operating systems, network protocols, and air traffic control systems. There is w...
Temporal Logics For Trace Systems: On Automated Verification
, 1993
"... We investigate an extension of CTL (Computation Tree Logic) by past modalities, called CTLP , interpreted over Mazurkiewicz's trace systems. The logic is powerful enough to express most of the partial order properties of distributed systems like serializability of database transactions, snapsho ..."
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Cited by 18 (7 self)
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We investigate an extension of CTL (Computation Tree Logic) by past modalities, called CTLP , interpreted over Mazurkiewicz's trace systems. The logic is powerful enough to express most of the partial order properties of distributed systems like serializability of database transactions, snapshots, parallel execution of program segments, or inevitability under concurrency fairness assumption. We show that the model checking problem for the logic is NPhard, even if past modalities cannot be nested. Then, we give a one exponential time model checking algorithm for the logic without nested past modalities. We show that all the interesting partial order properties can be model checked using our algorithm. Next, we show that it is possible to extend the model checking algorithm to cover the whole language and its extension to CTL*P . Finally, we prove that the logic is undecidable and we discuss consequences of our results on using propositional versions of partial order temporal logics to s...
Branching Time and Partial Order in Temporal Logics
 Time and Logic: A Computational Approach
, 1995
"... The aim of this paper is to present existing propositional temporal logics with branching and partially ordered time. These logics are used for specifying and proving properties of programs and systems. The branching time approach is useful e.g. for nondeterministic programs and can be applied ..."
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The aim of this paper is to present existing propositional temporal logics with branching and partially ordered time. These logics are used for specifying and proving properties of programs and systems. The branching time approach is useful e.g. for nondeterministic programs and can be applied also for concurrent programs. The partial order approach is especially useful for concurrent programs and allows one to study more subtle properties than those based on branching time. A survey of branching time logics, computation tree logics, partial order temporal logics and logics based on event structures is given. The following issues are concerned in this paper: the completeness of proof systems, the finite model property, decidability, model checking and expressiveness of the logics. 1 Introduction The aim of this paper is to present existing formal languages of propositional temporal logic with frames based on branching time structures or, more general, partial orders. Bran...
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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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...
Fair SMG and Linear Time Model Checking
 In Proceedings of Workshop on Automatic Verification Methods for Finite State Systems
, 1989
"... SMG is a system designed to generate a finite state model of a program from the program itself and an operational semantics for the programming language. This finite state model can then be modelchecked to verify desired temporal properties of the original program. In this paper we first show how w ..."
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Cited by 7 (4 self)
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SMG is a system designed to generate a finite state model of a program from the program itself and an operational semantics for the programming language. This finite state model can then be modelchecked to verify desired temporal properties of the original program. In this paper we first show how we have incorporated notions of fairness into SMG; in particular, a user is now able to define semantics with "fair" constructs, for example, parallel, repetitive choice, etc. The user can, indeed, mix different forms of fairness checking. Secondly we describe a practical approach to model checking of linear temporal formulae over the fair structures generated by SMG. Our approach is a refinement and extension of the fairsatisfiability algorithms, presented earlier by Lichtenstein and Pnueli, together with techniques developed in our practical implementations of decision procedures for linear temporal logic.
On Topological Hierarchies of Temporal Properties
, 1996
"... . The classification of properties of concurrent programs into safety and liveness was first proposed by Lamport [20]. Since then several characterizations of hierarchies of properties have been given, see e.g. [4, 18, 8, 19]; this includes syntactic characterizations (in terms classes of formula ..."
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. The classification of properties of concurrent programs into safety and liveness was first proposed by Lamport [20]. Since then several characterizations of hierarchies of properties have been given, see e.g. [4, 18, 8, 19]; this includes syntactic characterizations (in terms classes of formulas of logics such as the linear temporal logic) as well as extensional (as sets of computations in some abstract domain). The latter often admits a topological characterization with respect to the natural topologies of the domain of computations. We introduce a general notion of a linear time model of computation which consists of partial and completed computations satisfying certain axioms. The model is endowed with a natural topology. We show that the usual topologies on strings, Mazurkiewicz traces and pomsets arise as special cases. We then introduce a hierarchy of properties including safety, liveness, guarantee, response and persistence properties, and show that our definition ...
THE COMPLEXITY OF TREE AUTOMATA AND LOGICS OF PROGRAMS ∗
"... Abstract. The complexity of testing nonemptiness of finite state automata on infinite trees is investigated. It is shown that for tree automata with the pairs (or complemented pairs) acceptance condition having m states and n pairs, nonemptiness can be tested in deterministic time (mn) O(n); however ..."
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Abstract. The complexity of testing nonemptiness of finite state automata on infinite trees is investigated. It is shown that for tree automata with the pairs (or complemented pairs) acceptance condition having m states and n pairs, nonemptiness can be tested in deterministic time (mn) O(n); however, it is shown that the problem is in general NPcomplete (or coNPcomplete, respectively). The new nonemptiness algorithm yields exponentially improved, essentially tight upper bounds for numerous important modal logics of programs, interpreted with the usual semantics over structures generated by binary relations. For example, it follows that satisfiability for the full branching time logic CTL ∗ can be tested in deterministic double exponential time. Another consequence is that satisfiability for propositional dynamic logic (PDL) with a repetition construct (PDLdelta) and for the propositional Mucalculus (Lµ) can be tested in deterministic single exponential time.