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445
Complexity of Metric Temporal Logics with Counting and the Pnueli Modalities
"... Abstract. The common metric temporal logics for continuous time were shown to be insufficient, when it was proved in [7, 12] that they cannot express a modality suggested by Pnueli. Moreover no temporal logic with a finite set of modalities can express all the natural generalizations of this modalit ..."
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Cited by 3 (0 self)
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Abstract. The common metric temporal logics for continuous time were shown to be insufficient, when it was proved in [7, 12] that they cannot express a modality suggested by Pnueli. Moreover no temporal logic with a finite set of modalities can express all the natural generalizations
On the decidability of metric temporal logic
 In Proc. LICS
, 2005
"... Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with nonprimitive recursive complexity. We also consider the modelchecking problem for MTL: whether all w ..."
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Cited by 68 (10 self)
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Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with nonprimitive recursive complexity. We also consider the modelchecking problem for MTL: whether all
Integrating Metric and Qualitative Temporal Reasoning
 IN PROCEEDINGS OF AAAI91
, 1991
"... Research in Artificial Intelligence on constraintbased representations for temporal reasoning has largely concentrated on two kinds of formalisms: systems of simple linear inequalities to encode metric relations between time points, and systems of binary constraints in Allen's temporal calculu ..."
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Cited by 117 (4 self)
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Research in Artificial Intelligence on constraintbased representations for temporal reasoning has largely concentrated on two kinds of formalisms: systems of simple linear inequalities to encode metric relations between time points, and systems of binary constraints in Allen's temporal
When is Metric Temporal Logic Expressively Complete? ∗
"... A seminal result of Kamp is that over the reals Linear Temporal Logic (LTL) has the same expressive power as firstorder logic with binary order relation < and monadic predicates. A key question is whether there exists an analogue of Kamp’s theorem for Metric Temporal Logic (MTL) – a generalizati ..."
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Cited by 2 (2 self)
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A seminal result of Kamp is that over the reals Linear Temporal Logic (LTL) has the same expressive power as firstorder logic with binary order relation < and monadic predicates. A key question is whether there exists an analogue of Kamp’s theorem for Metric Temporal Logic (MTL) – a
Metric Temporal Logic with Durations
 Computer Science, special issue on hybrid systems
, 1994
"... . We present a formal framework based on metric temporal logic (MTL) for specifying and verifying realtime systems with a continuous environment. Metric temporal logic is extended to allow specification of properties about duration of system's states. We prove that every formula of the duratio ..."
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Cited by 7 (1 self)
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. We present a formal framework based on metric temporal logic (MTL) for specifying and verifying realtime systems with a continuous environment. Metric temporal logic is extended to allow specification of properties about duration of system's states. We prove that every formula
Executing Metric Temporal Logic
 Theoretical Computer Science
, 1997
"... this paper, we present a solution to the problem of supporting derivability in metric temporal logic based on a settheoretic translation method. In order to execute metric temporal logic, we first transforms it into a polymodal logic with infinitely many modalities, and then reduces derivability in ..."
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Cited by 4 (4 self)
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this paper, we present a solution to the problem of supporting derivability in metric temporal logic based on a settheoretic translation method. In order to execute metric temporal logic, we first transforms it into a polymodal logic with infinitely many modalities, and then reduces derivability
TwoSorted Metric Temporal Logics
 Theoretical Computer Science
, 1995
"... Temporal logic has been successfully used for modeling and analyzing the behavior of reactive and concurrent systems. Standard temporal logic is inadequate for realtime applications because it only deals with qualitative timing properties. This is overcome by metric temporal logics which offer a ..."
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Cited by 9 (7 self)
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Temporal logic has been successfully used for modeling and analyzing the behavior of reactive and concurrent systems. Standard temporal logic is inadequate for realtime applications because it only deals with qualitative timing properties. This is overcome by metric temporal logics which offer
Coverage metrics for temporal logic model checking
 in Lecture Notes in Computer Science
, 2001
"... Abstract. In formal verification, we verify that a system is correct with respect to a specification. Even when the system is proven to be correct, there is still a question of how complete the specification is, and whether it really covers all the behaviors of the system. In this paper we study cov ..."
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Cited by 36 (14 self)
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coverage metrics for model checking. Coverage metrics are based on modifications we apply to the system in order to check which parts of it were actually relevant for the verification process to succeed. We introduce two principles that we believe should be part of any coverage metric for model checking: a
Bounded Variability of Metric Temporal Logic
, 2013
"... Previous work has shown that reasoning with realtime temporal logics is often simpler when restricted to models with bounded variability—where no more than v events may occur every V time units, for given v, V. When reasoning about formulas with intrinsic bounded variability, one can employ the sim ..."
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the simpler techniques that rely on bounded variability, without any loss of generality. What is then the complexity of algorithmically deciding which formulas have intrinsic bounded variability? In this paper, we study the problem with reference to Metric Temporal Logic (MTL). We prove that deciding bounded
Online Monitoring of Metric Temporal Logic
"... Abstract. Current approaches to monitoring realtime properties suffer either from unbounded space requirements or lack of expressiveness. In this paper, we adapt a separation technique enabling us to rewrite arbitrary MTL formulas into LTL formulas over a set of atoms comprising bounded MTL formu ..."
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Abstract. Current approaches to monitoring realtime properties suffer either from unbounded space requirements or lack of expressiveness. In this paper, we adapt a separation technique enabling us to rewrite arbitrary MTL formulas into LTL formulas over a set of atoms comprising bounded MTL formulas. As a result, we obtain the first tracelength independent online monitoring procedure for full MTL. 1
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