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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 250 (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.
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 220 (15 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.
Planning for Temporally Extended Goals
, 1997
"... this paper appears in Proceedings of AAAI '96, pp. 12151222. F. Bacchus and F. Kabanza / Temporally Extended Goals 2 Yet this flexibility also poses a problem: how do we communicate to such an agent the task we want accomplished in a sufficiently precise manner so that it does what we really ..."
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Cited by 159 (10 self)
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this paper appears in Proceedings of AAAI '96, pp. 12151222. F. Bacchus and F. Kabanza / Temporally Extended Goals 2 Yet this flexibility also poses a problem: how do we communicate to such an agent the task we want accomplished in a sufficiently precise manner so that it does what we really
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 symboli ..."
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Cited by 146 (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.
What Good Are Digital Clocks?
, 1992
"... . Realtime systems operate in "real," continuous time and state changes may occur at any realnumbered time point. Yet many verification methods are based on the assumption that states are observed at integer time points only. What can we conclude if a realtime system has been shown ..."
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Cited by 143 (14 self)
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. Realtime systems operate in "real," continuous time and state changes may occur at any realnumbered time point. Yet many verification methods are based on the assumption that states are observed at integer time points only. What can we conclude if a realtime system has been shown "correct" for integral observations? Integer time verification techniques suffice if the problem of whether all realnumbered behaviors of a system satisfy a property can be reduced to the question of whether the integral observations satisfy a (possibly modified) property. We show that this reduction is possible for a large and important class of systems and properties: the class of systems includes all systems that can be modeled as timed transition systems; the class of properties includes timebounded invariance and timebounded response. 1 Introduction Over the past few years, we have seen a proliferation of formal methodologies for software and hardware design that emphasize the treatm...
EventClock Automata: A Determinizable Class of Timed Automata
 Theoretical Computer Science
, 1999
"... We introduce eventrecording automata. An eventrecording automaton is a timed automaton that contains, for every event a, a clock that records the time of the last occurrence of a. The class of eventrecording automata is, on one hand, expressive enough to model (finite) timed transition systems an ..."
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Cited by 121 (2 self)
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We introduce eventrecording automata. An eventrecording automaton is a timed automaton that contains, for every event a, a clock that records the time of the last occurrence of a. The class of eventrecording automata is, on one hand, expressive enough to model (finite) timed transition systems and, on the other hand, determinizable and closed under all boolean operations. As a result, the language inclusion problem is decidable for eventrecording automata. We present a translation from timed transition systems to eventrecording automata, which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors. We also consider eventpredicting automata, which contain clocks that predict the time of the next occurrence of an event. The class of eventclock automata, which contain both eventrecording and eventpredicting clocks, is a suitable specification language for realtime properties. We provide an algorithm for checking if a timed automa...
TALplanner: A temporal logic based forward chaining planner
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 2001
"... We present TALplanner, a forwardchaining planner based on the use of domaindependent
search control knowledge represented as formulas in the Temporal Action
Logic (TAL). TAL is a narrative based linear metric time logic used for reasoning
about action and change in incompletely speci#12;ed dynamic ..."
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Cited by 95 (17 self)
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We present TALplanner, a forwardchaining planner based on the use of domaindependent
search control knowledge represented as formulas in the Temporal Action
Logic (TAL). TAL is a narrative based linear metric time logic used for reasoning
about action and change in incompletely speci#12;ed dynamic environments. TAL
is used as the formal semantic basis for TALplanner, where a TAL goal narrative
with control formulas is input to TALplanner which then generates a TAL narrative
that entails the goal and control formulas. The sequential version of TALplanner is
presented. The expressivity of plan operators is then extended to deal with an interesting
class of resource types. An algorithm for generating concurrent plans, where
operators have varying durations and internal state, is also presented. All versions
of TALplanner have been implemented. The potential of these techniques is demonstrated
by applying TALplanner to a number of standard planning benchmarks in
the literature.
Robust timed automata
 In Proceedings of HART 97
, 1997
"... Abstract. We de ne robust timed automata, which are timed automata that accept all trajectories \robustly": if a robust timed automaton accepts a trajectory, then it must accept neighboring trajectories also � and if a robust timed automaton rejects a trajectory, thenitmust reject neighbori ..."
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Cited by 57 (6 self)
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Abstract. We de ne robust timed automata, which are timed automata that accept all trajectories \robustly&quot;: if a robust timed automaton accepts a trajectory, then it must accept neighboring trajectories also � and if a robust timed automaton rejects a trajectory, thenitmust reject neighboring trajectories also. We show that the emptiness problem for robust timed automata is still decidable, by modifying the region construction for timed automata. We then show that, like timed automata, robust timed automata cannot be determinized. This result is somewhat unexpected, given that in temporal logic, the removal of realtime equality constraints is known to lead to a decidable theory that is closed under all boolean operations. 1
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 47 (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...
Computing Accumulated Delays in Realtime Systems
, 1993
"... . We present a verification algorithm for duration properties of realtime systems. While simple realtime properties constrain the total elapsed time between events, duration properties constrain the accumulated satisfaction time of state predicates. We formalize the concept of durations by introdu ..."
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Cited by 43 (6 self)
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. We present a verification algorithm for duration properties of realtime systems. While simple realtime properties constrain the total elapsed time between events, duration properties constrain the accumulated satisfaction time of state predicates. We formalize the concept of durations by introducing duration measures for timed automata. A duration measure assigns to each finite run of a timed automaton a real number the duration of the run which may be the accumulated satisfaction time of a state predicate along the run. Given a timed automaton with a duration measure, an initial and a final state, and an arithmetic constraint, the durationbounded reachability problem asks if there is a run of the automaton from the initial state to the final state such that the duration of the run satisfies the constraint. Our main result is an (optimal) Pspace decision procedure for the durationbounded reachability problem. 1 Introduction Over the past decade, model checking [CE81, QS81]...