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31
A Really Temporal Logic
 Journal of the ACM
, 1989
"... . We introduce a temporal logic for the specification of realtime systems. Our logic, TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier binds a variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable f ..."
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Cited by 238 (26 self)
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. We introduce a temporal logic for the specification of realtime systems. Our logic, TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier binds a variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable formalism for verification. We present a tableaubased decision procedure and a model checking algorithm for TPTL. Several generalizations of TPTL are shown to be highly undecidable. 1 Introduction Linear temporal logic is a widely accepted language for specifying properties of reactive systems and their behavior over time [Pnu77, OL82, MP92]. The tableaubased satisfiability algorithm for its propositional version, PTL, forms the basis for the automatic verification and synthesis of finitestate systems [LP84, MW84]. PTL is interpreted over models that abstract away from the actual times at which events occur, retaining only temporal ordering information about the states of a system. The a...
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.
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 201 (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 182 (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.
Equivalence of Measures of Complexity Classes
"... The resourcebounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Specifically, for any real number ffi ? 0, any uniformly polynomialtime computable sequence ~ fi = (fi 0 ; fi 1 ; fi 2 ; : : : ) of real numbers (biases ..."
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Cited by 71 (19 self)
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The resourcebounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Specifically, for any real number ffi ? 0, any uniformly polynomialtime computable sequence ~ fi = (fi 0 ; fi 1 ; fi 2 ; : : : ) of real numbers (biases) fi i 2 [ffi; 1 \Gamma ffi], and any complexity class C (such as P, NP, BPP, P/Poly, PH, PSPACE, etc.) that is closed under positive, polynomialtime, truthtable reductions with queries of at most linear length, it is shown that the following two conditions are equivalent. (1) C has pmeasure 0 (respectively, measure 0 in E, measure 0 in E 2 ) relative to the cointoss probability measure given by the sequence ~ fi. (2) C has pmeasure 0 (respectively, measure 0 in E, measure 0 in E 2 ) relative to the uniform probability measure. The proof introduces three techniques that may be useful in other contexts, namely, (i) the transformation of an efficient martingale for one probability measu...
Incremental concept learning for bounded data mining
 Information and Computation
, 1999
"... Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning ma ..."
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Cited by 39 (29 self)
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Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning machine computes a sequence of hypotheses about the target concept from a positive presentation of it. With iterative learning, the learning machine, in making a conjecture, has access to its previous conjecture and the latest data item coming in. In kbounded examplememory inference (k is a priori xed) the learner is allowed to access, in making a conjecture, its previous hypothesis, its memory of up to k data items it has already seen, and the next element coming in. In the case of kfeedback identi cation, the learning machine, in making a conjecture, has access to its previous conjecture, the latest data item coming in, and, on the basis of this information, it can compute k items and query the database of previous data to nd out, for each of the k items, whether or not it is in the database (k is again a priori xed). In all cases, the sequence of conjectures has to converge to a hypothesis
Recursive computational depth
 Information and Computation
, 1999
"... In the 1980's, Bennett introduced computational depth as a formal measure of the amount of computational history that is evident in an object's structure. In particular, Bennett identi ed the classes of weakly deep and strongly deep sequences, and showed that the halting problem is strongly deep. Ju ..."
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Cited by 18 (2 self)
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In the 1980's, Bennett introduced computational depth as a formal measure of the amount of computational history that is evident in an object's structure. In particular, Bennett identi ed the classes of weakly deep and strongly deep sequences, and showed that the halting problem is strongly deep. Juedes, Lathrop, and Lutz subsequently extended this result by de ning the class of weakly useful sequences, and proving that every weakly useful sequence is strongly deep. The present paper investigates re nements of Bennett's notions of weak and strong depth, called recursively weak depth (introduced by Fenner, Lutz and Mayordomo) and recursively strong depth (introduced here). It is argued that these re nements naturally capture Bennett's idea that deep objects are those which \contain internal evidence of a nontrivial causal history. " The fundamental properties of recursive computational depth are developed, and it is shown that the recursively weakly (respectively, strongly) deep sequences form a proper subclass of the class of weakly (respectively, strongly) deep sequences. The abovementioned theorem of Juedes, Lathrop, and Lutz is then strengthened by proving that every weakly useful sequence is recursively strongly deep. It follows from these results that not every strongly deep sequence is weakly useful, thereby answering a question posed by Juedes.
Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 18 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re
Computational Limits on Team Identification of Languages
, 1993
"... A team of learning machines is essentially a multiset of learning machines. ..."
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Cited by 17 (7 self)
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A team of learning machines is essentially a multiset of learning machines.
The intrinsic complexity of language identification
 Journal of Computer and System Sciences
, 1996
"... A new investigation of the complexity of language identification is undertaken using the notion of reduction from recursion theory and complexity theory. The approach, referred to as the intrinsic complexity of language identification, employs notions of ‘weak ’ and ‘strong ’ reduction between learn ..."
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Cited by 17 (7 self)
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A new investigation of the complexity of language identification is undertaken using the notion of reduction from recursion theory and complexity theory. The approach, referred to as the intrinsic complexity of language identification, employs notions of ‘weak ’ and ‘strong ’ reduction between learnable classes of languages. The intrinsic complexity of several classes is considered and the results agree with the intuitive difficulty of learning these classes. Several complete classes are shown for both the reductions and it is also established that the weak and strong reductions are distinct. An interesting result is that the self referential class of Wiehagen in which the minimal element of every language is a grammar for the language and the class of pattern languages introduced by Angluin are equivalent in the strong sense. This study has been influenced by a similar treatment of function identification by Freivalds, Kinber, and Smith. 1