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142
An automatatheoretic approach to linear temporal logic
 Logics for Concurrency: Structure versus Automata, volume 1043 of Lecture Notes in Computer Science
, 1996
"... Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over s ..."
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Cited by 217 (23 self)
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Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over some alphabet. Thus,programs and specificationscan be viewed as descriptions of languagesover some alphabet. The automatatheoretic perspective considers the relationships between programs and their specifications as relationships between languages.By translating programs and specifications to automata, questions about programs and their specifications can be reduced to questions about automata. More specifically, questions such as satisfiability of specifications and correctness of programs with respect to their specifications can be reduced to questions such as nonemptiness and containment of automata. Unlike classical automata theory, which focused on automata on finite words, the applications to program specification, verification, and synthesis, use automata on infinite words, since the computations in which we are interested are typically infinite. This paper provides an introduction to the theory of automata on infinite words and demonstrates its applications to program specification, verification, and synthesis. 1
Tree Automata, MuCalculus and Determinacy (Extended Abstract)
 IN PROCEEDINGS OF THE 32ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, FOCS ’91
, 1991
"... We show that the propositional MuCalculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the MuCalculus, our equivalence provides a radically simplified, alternative proof of Rabin's complementation lemma for tree automata, which is the ..."
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Cited by 215 (4 self)
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We show that the propositional MuCalculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the MuCalculus, our equivalence provides a radically simplified, alternative proof of Rabin's complementation lemma for tree automata, which is the heart of one of the deepest decidability results. We also show how MuCalculus can be used to establish determinacy of infinite games used in earlier proofs of complementation lemma, and certain games used in the theory of online algorithms.
The Dimensions of Individual Strings and Sequences
 INFORMATION AND COMPUTATION
, 2003
"... A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive dimension is used to assign every individual (infinite, binary ..."
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Cited by 93 (10 self)
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A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive dimension is used to assign every individual (infinite, binary) sequence S a dimension, which is a real number dim(S) in the interval [0, 1]. Sequences that
The History and Status of the P versus NP Question
, 1992
"... this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the re ..."
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Cited by 50 (0 self)
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this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the realization that certain problems are algorithmically unsolvable. At around this time, forerunners of the programmable computing machine were beginning to appear. As mathematicians contemplated the practical capabilities and limitations of such devices, computational complexity theory emerged from the theory of algorithmic unsolvability. Early on, a particular type of computational task became evident, where one is seeking an object which lies
An Undetectable Computer Virus
 In Proceedings of Virus Bulletin Conference
, 2000
"... One of the few solid theoretical results in the study of computer viruses is Cohen's 1987 demonstration that there is no algorithm that can perfectly detect all possible viruses [1]. This brief paper adds to the bad news, by pointing out that there are computer viruses which no algorithm can detect, ..."
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Cited by 33 (0 self)
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One of the few solid theoretical results in the study of computer viruses is Cohen's 1987 demonstration that there is no algorithm that can perfectly detect all possible viruses [1]. This brief paper adds to the bad news, by pointing out that there are computer viruses which no algorithm can detect, even under a somewhat more liberal definition of detection. We also comment on the senses of "detect" used in these results, and note that the immediate impact of these results on computer virus detection in the real world is small.
The classification of hypersmooth Borel equivalence relations
 J. Amer. Math. Soc
, 1997
"... This paper is a contribution to the study of Borel equivalence relations in standard Borel spaces, i.e., Polish spaces equipped with their Borel structure. A class of such equivalence relations which has received particular attention is the class of hyperfinite Borel equivalence relations. These can ..."
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Cited by 30 (4 self)
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This paper is a contribution to the study of Borel equivalence relations in standard Borel spaces, i.e., Polish spaces equipped with their Borel structure. A class of such equivalence relations which has received particular attention is the class of hyperfinite Borel equivalence relations. These can be defined as the increasing unions of sequences of Borel equivalence relations all of whose equivalence classes are finite or, as it turns out, equivalently those induced by the orbits of a single Borel automorphism. Hyperfinite equivalence relations have been classified in [DJK], under two notions of equivalence, Borel bireducibility, and Borel isomorphism. An equivalence relation E on X is Borel reducible to an equivalence relation F on Y if there is a Borel map f: X → Y with xEy ⇔ f(x)Ff(y). We write then E ≤ F. If E ≤ Fand F ≤ E we say that E,F are Borel bireducible, in symbols E ≈ ∗ F.When E ≈ ∗ Fthe quotient spaces X/E, Y/F have the same “effective ” or “definable ” cardinality. We say that E,F are Borel isomorphic if there exists a Borel bijection f: X → Y with xEy ⇔ f(x)Ff(y). Below we denote by E0,Et the equivalence relations on the Cantor space 2 N given by: xE0y ⇔
Logical Specifications of Infinite Computations
 A Decade of Concurrency: Reflections and Perspectives, volume 803 of LNCS
, 1993
"... . Starting from an identification of infinite computations with ! words, we present a framework in which different classification schemes for specifications are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recu ..."
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Cited by 20 (2 self)
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. Starting from an identification of infinite computations with ! words, we present a framework in which different classification schemes for specifications are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recursion theory, and with the hierarchy of acceptance conditions of !automata. In particular, it is shown in which sense these hierarchies can be viewed as classifications of logical formulas by the complexity measure of quantifier alternation. In this context, the automaton theoretic approach to logical specifications over !words turns out to be a technique to reduce quantifier complexity of formulas. Finally, we indicate some perspectives of this approach, discuss variants of the logical framework (firstorder logic, temporal logic), and outline the effects which arise when branching computations are considered (i.e., when infinite trees instead of !words are taken as model of computation)...
New Directions In Descriptive Set Theory
 Bull. Symbolic Logic
, 1999
"... This article is based on the G odel Lecture given at the meeting of the Association for Symbolic Logic at Toronto in April 1998. Research and preparation for this paper were supported in part by NSF Grant DMS 9619880. ..."
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Cited by 18 (5 self)
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This article is based on the G odel Lecture given at the meeting of the Association for Symbolic Logic at Toronto in April 1998. Research and preparation for this paper were supported in part by NSF Grant DMS 9619880.
Towards Abstractions for Distributed Systems
, 2004
"... For historical, sociological and technical reasons, calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equa ..."
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Cited by 17 (5 self)
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For historical, sociological and technical reasons, calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equally convincing formal foundation for distributed computing has not been forthcoming. This thesis seeks to contribute towards ameliorating that omission. To this end, guided by the assumption that distributed computing is concurrent computing with partial failures of various kinds, we extend the asynchronous calculus with a notion of sites, the possibility of site failure, a persistence mechanism to deal with site failures, the distinction between intersite and intrasite communication, the possibility of message loss in intersite communication and a timer construct, as is often used in distributed algorithms to deal with various failure scenarios.
Simple cardinal characteristics of the continuum, in: Set theory of the reals
 Israel Math. Conf. Proc. 6, BarIlan Univ., Ramat
, 1993
"... Abstract. We classify many cardinal characteristics of the continuum according to the complexity, in the sense of descriptive set theory, of their definitions. The simplest characteristics (Σ0 2 and, under suitable restrictions, Π0 2) are shown to have pleasant properties, related to Baire category. ..."
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Cited by 13 (1 self)
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Abstract. We classify many cardinal characteristics of the continuum according to the complexity, in the sense of descriptive set theory, of their definitions. The simplest characteristics (Σ0 2 and, under suitable restrictions, Π0 2) are shown to have pleasant properties, related to Baire category. We construct models of set theory where (unrestricted) Π0 2characteristics behave quite chaotically and no new characteristics appear at higher complexity levels. We also discuss some characteristics associated with partition theorems and we present, in an appendix, a simplified proof of Shelah’s theorem that the dominating number is less than or equal to the independence number. 1.