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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 203 (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 Benefits of Relaxing Punctuality
, 1996
"... The most natural, compositional, way of modeling realtime systems uses a dense domain for time. The satis ability of timing constraints that are capable of expressing punctuality in this model, however, is known to be undecidable. We introduce a temporal language that can constrain the time differe ..."
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Cited by 202 (18 self)
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The most natural, compositional, way of modeling realtime systems uses a dense domain for time. The satis ability of timing constraints that are capable of expressing punctuality in this model, however, is known to be undecidable. We introduce a temporal language that can constrain the time difference between events only with finite, yet arbitrary, precision and show the resulting logic to be EXPSPACEcomplete. This result allows us to develop an algorithm for the verification of timing properties of realtime systems with a dense semantics.
Logics and Models of Real Time: A Survey
"... We survey logicbased and automatabased languages and techniques for the specification and verification of realtime systems. In particular, we discuss three syntactic extensions of temporal logic: timebounded operators, freeze quantification, and time variables. We also discuss the extension of ..."
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Cited by 183 (16 self)
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We survey logicbased and automatabased languages and techniques for the specification and verification of realtime systems. In particular, we discuss three syntactic extensions of temporal logic: timebounded operators, freeze quantification, and time variables. We also discuss the extension of finitestate machines with clocks and the extension of transition systems with time bounds on the transitions. All of the resulting notations can be interpreted over a variety of different models of time and computation, including linear and branching time, interleaving and true concurrency, discrete and continuous time. For each choice of syntax and semantics, we summarize the results that are known about expressive power, algorithmic finitestate verification, and deductive verification.
Parametric realtime reasoning
 IN PROCEEDINGS OF THE 25TH ANNUAL SYMPOSIUM ON THEORY OF COMPUTING
, 1993
"... Traditional approaches to the algorithmic verification of realtime systems are limited to checking program correctness with respect to concrete timing properties (e.g., "message delivery within 10 milliseconds"). We address the more realistic and more ambitious problem of deriving symbolic constrai ..."
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Cited by 96 (6 self)
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Traditional approaches to the algorithmic verification of realtime systems are limited to checking program correctness with respect to concrete timing properties (e.g., "message delivery within 10 milliseconds"). We address the more realistic and more ambitious problem of deriving symbolic constraints on the timing properties required of realtime systems (e.g., "message delivery within the time it takes to execute two assignment statements"). To model this problem, we introduce parametric timed automata  finitestate machines whose transitions are constrained with parametric timing requirements. The emptiness question for parametric timed automata is central to the verification problem. On the negative side, we show that in general this question is undecidable. On the positive side, we provide algorithms for checking the emptiness of restricted classes of parametric timed automata. The practical relevance of these classes is illustrated with several verification examples. There remains a gap between the automata classes for which we know that emptiness is decidable and undecidable, respectively, and this gap is related to various hard and open problems of logic and automata theory.
TimeConstrained Automata
 CONCUR '91: 2nd International Conference on Concurrency Theory, volume 527 of Lecture Notes in Computer Science
, 1991
"... ) Michael Merritt AT&T Bell Laboratories 600 Mountain Avenue Murray Hill, NJ 07974 merritt@research.att.com Francesmary Modugno School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 fmm@cs.cmu.edu Mark R. Tuttle DEC Cambridge Research Lab One Kendall Sq., Bldg. 700 Cambridg ..."
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Cited by 83 (0 self)
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) Michael Merritt AT&T Bell Laboratories 600 Mountain Avenue Murray Hill, NJ 07974 merritt@research.att.com Francesmary Modugno School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 fmm@cs.cmu.edu Mark R. Tuttle DEC Cambridge Research Lab One Kendall Sq., Bldg. 700 Cambridge, MA 02139 tuttle@crl.dec.com Abstract In this paper, we augment the inputoutput automaton model in order to reason about time in concurrent systems, and we prove simple properties of this augmentation. The inputoutput automata model is a useful model for reasoning about computation in concurrent and distributed systems because it allows fundamental properties such as fairness and compositionality to be expressed easily and naturally. A unique property of the model is that systems are modeled as the composition of autonomous components. This paper describes a way to add a notion of time to the model in a way that preserves these properties. The result is a simple, compositional model fo...
An Implementation of Three Algorithms for Timing Verification Based on Automata Emptiness
, 1992
"... This papers describes modifications to and the implementation of algorithms previously described in [1, 11]. We first describe three generic (untimed) algorithms for constructing graphs of the reachable states of a system, and how these graphs can be used for verification. They all have as input an ..."
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Cited by 57 (3 self)
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This papers describes modifications to and the implementation of algorithms previously described in [1, 11]. We first describe three generic (untimed) algorithms for constructing graphs of the reachable states of a system, and how these graphs can be used for verification. They all have as input an implicit description of a transition system. We then apply these algorithms to realtime systems. The first algorithm performs a straightforward reachability analysis on sets of states of the system, rather than on individual states. This corresponds to stepping symbolically through the system many states at a time. In the case of a realtime system this procedure constructs a graph where each node is the union of some regions of the regions graph. There is therefore no need for an a priori partitioning of the state space into individual regions; however, this approach potentially leads to exponentially worse complexity since its potential state space is the power set of regions [1]. The other two algorithms we consider are minimization algorithms [12, 13, 11]. These simultaneously perform reachability analysis and minimization from an implicit system description. These can lead to great savings when the minimized graph is much smaller than the explicit reachable graph. Our paradigm for verification is to test for the emptiness of the set of all timed system executions that violate a requirements specification. One way to specify and verify nonterminating processes is to model them as languages of !sequences of events [14, 15, 16, 1, 17, 18]. Modular processes can be constructed via composition operations involving language intersection. Specifications are also given as languages: they contain all acceptable event sequences. Program correctness is then just language contain...
Specifying Timed State Sequences in Powerful Decidable Logics and Timed Automata (Extended Abstract)
 LNCS 863
, 1994
"... ) Thomas Wilke ChristianAlbrechtsUniversitat zu Kiel, Institut fur Informatik und Praktische Mathematik, D24098 Kiel, Germany ? Abstract. A monadic secondorder language, denoted by Ld, is introduced for the specification of sets of timed state sequences. A fragment of Ld, denoted by L $ d, is ..."
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Cited by 52 (0 self)
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) Thomas Wilke ChristianAlbrechtsUniversitat zu Kiel, Institut fur Informatik und Praktische Mathematik, D24098 Kiel, Germany ? Abstract. A monadic secondorder language, denoted by Ld, is introduced for the specification of sets of timed state sequences. A fragment of Ld, denoted by L $ d, is proved to be expressively complete for timed automata (Alur and Dill), i. e., every timed regular language is definable by a L $ dformula and every L $ dformula defines a timed regular language. As a consequence the satisfiability problem for L $ d is decidable. Timed temporal logics are shown to be effectively embeddable into L $ d and hence turn out to have a decidable theory. This applies to TL \Gamma (Manna and Pnueli) and EMITLp , which is obtained by extending the logic MITLp (Alur and Henzinger) by automata operators (Sistla, Vardi, and Wolper). For every positive natural number k the full monadic secondorder logic Ld and L $ d are equally expressive modulo the set of timed...
Timing Verification by Successive Approximation
 INFORMATION AND COMPUTATION
, 1995
"... We present an algorithm for verifying that a model M with timing constraints satisfies a given temporal property T . The model M is given as a parallel composition of !automata P i , where each automaton P i is constrained by bounds on delays. The property T is given as an !automaton as well, and ..."
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Cited by 44 (11 self)
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We present an algorithm for verifying that a model M with timing constraints satisfies a given temporal property T . The model M is given as a parallel composition of !automata P i , where each automaton P i is constrained by bounds on delays. The property T is given as an !automaton as well, and the verification problem is posed as a language inclusion question L(M ) ` L(T ). In constructing the composition M of the constrained automata P i , one needs to rule out the behaviors that are inconsistent with the delay bounds, and this step is (provably) computationally expensive. We propose an iterative solution which involves generating successive approximations M j to M , with containment L(M ) ` L(M j ) and monotone convergence L(M j ) ! L(M ) within a bounded number of steps. As the succession progresses, the approximations M j become more complex. At any step of the iteration one may get a proof or a counterexample to the original language inclusion question. The described algori...
Verifying Automata Specifications of Probabilistic Realtime Systems
 RealTime: Theory in Practice, Springer LNCS 600
, 1991
"... . We present a modelchecking algorithm for a system presented as a generalized semiMarkov process and a specification given as a deterministic timed automaton. This leads to a method for automatic verification of timing properties of finitestate probabilistic realtime systems. Keywords: Realti ..."
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Cited by 35 (3 self)
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. We present a modelchecking algorithm for a system presented as a generalized semiMarkov process and a specification given as a deterministic timed automaton. This leads to a method for automatic verification of timing properties of finitestate probabilistic realtime systems. Keywords: Realtime, Probabilistic systems, Automatic verification. 1 Introduction There is increasing awareness that unexpected behavior from interacting processes can cause serious problems. This observation applies not only to programs and digital systems, but also to physical processes, such as robots, automobiles, manufacturing processes, and so on. Indeed, as digital systems become smaller and cheaper, their use to control and interact with physical processes will inevitably increase. Formal verification of these systems seeks mathematical methods for reasoning about their behavior. Automatic formal verification is particularly promising, because it requires far less labor than the manual techniques. ...