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The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Three Thresholds for a Liar
 Combinatorics, Probability and Computing
, 1992
"... Motivated by the problem of making correct computations from partly false information, we study a corruption of the classic game "Twenty Questions" in which the player who answers the yesorno questions is permitted to lie up to a fixed fraction r of the time. The other player is allowed q arbitrar ..."
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Cited by 20 (1 self)
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Motivated by the problem of making correct computations from partly false information, we study a corruption of the classic game "Twenty Questions" in which the player who answers the yesorno questions is permitted to lie up to a fixed fraction r of the time. The other player is allowed q arbitrary questions with which to try to determine, with certainty, which of n objects his opponent has in mind; he "wins" if he can always do so, and "wins quickly" if he can do so using only O(log n) questions. It turns out that there is a threshold value for r below which the querier can win quickly, and above which he cannot win at all. However, the threshold value varies according to the precise rules of the game. Our "three thresholds theorem" says that when the answerer is forbidden at any point to have answered more than a fraction r of the questions incorrectly, then the threshold value is r = 1 2 ; when the requirement is merely that the total number of lies cannot exceed rq, the threshol...
Improved File Synchronization Techniques for Maintaining Large Replicated Collections over Slow Networks
 IN PROC. OF THE INT. CONF. ON DATA ENGINEERING
, 2004
"... We study the problem of maintaining large replicated collections of files or documents in a distributed environment with limited bandwidth. This problem arises in a number of important applications, such as synchronization of data between accounts or devices, content distibution and web caching netw ..."
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Cited by 18 (5 self)
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We study the problem of maintaining large replicated collections of files or documents in a distributed environment with limited bandwidth. This problem arises in a number of important applications, such as synchronization of data between accounts or devices, content distibution and web caching networks, web site mirroring, storage networks, and large scale web search and mining. At the core of the problem lies the following challenge, called the file synchronization problem: given two versions of a file on different machines, say an outdated and a current one, how can we update the outdated version with minimum communication cost, by exploiting the significant similarity between the versions? While a popular open source tool for this problem called rsync is used in hundreds of thousands of installations, there have been only very few attempts to improve upon this tool in practice. In this paper,
Animal Foraging and the Evolution of GoalDirected Cognition
 Cognitive Science
, 2006
"... Foraging and feedingrelated behaviors across eumetazoans share similar molecular mechanisms, suggesting the early evolution of an optimal foraging behavior called arearestricted search (ARS), involving mechanisms of dopamine and glutamate in the modulation of behavioral focus. Similar mechanisms ..."
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Cited by 17 (7 self)
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Foraging and feedingrelated behaviors across eumetazoans share similar molecular mechanisms, suggesting the early evolution of an optimal foraging behavior called arearestricted search (ARS), involving mechanisms of dopamine and glutamate in the modulation of behavioral focus. Similar mechanisms in the vertebrate basal ganglia control motor behavior and cognition and reveal an evolutionary progression toward increasing internal connections between prefrontal cortex and striatum in moving from amphibian to primate. The basal ganglia in higher vertebrates show the ability to transfer dopaminergic activity from unconditioned stimuli to conditioned stimuli. The evolutionary role of dopamine in the modulation of goaldirected behavior and cognition is further supported by pathologies of human goaldirected cognition, which have motor and cognitive dysfunction and organize themselves, with respect to dopaminergic activity, along the gradient described by ARS, from perseverative to unfocused. The evidence strongly supports the evolution of goaldirected cognition out of mechanisms initially in control of spatial foraging but, through increasing cortical connections, eventually used to forage for information.
Understanding Mathematical Discourse
 Dialogue. Amsterdam University
, 1999
"... Discourse Understanding is hard. This seems to be especially true for mathematical discourse, that is proofs. Restricting discourse to mathematical discourse allow us, however, to study the subject matter in its purest form. This domain of discourse is rich and welldefined, highly structured, offers ..."
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Cited by 7 (6 self)
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Discourse Understanding is hard. This seems to be especially true for mathematical discourse, that is proofs. Restricting discourse to mathematical discourse allow us, however, to study the subject matter in its purest form. This domain of discourse is rich and welldefined, highly structured, offers a welldefined set of discourse relations and forces/allows us to apply mathematical reasoning. We give a brief discussion on selected linguistic phenomena of mathematical discourse, and an analysis from the mathematician’s point of view. Requirements for a theory of discourse representation are given, followed by a discussion of proofs plans that provide necessary context and structure. A large part of semantics construction is defined in terms of proof plan recognition and instantiation by matching and attaching. 1
Sorting and Selection with Imprecise Comparisons
"... Abstract. In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences amongst n elements of a human subject. The method requires performing all ( n 2 comparisons then sorting elements according to the number of wins. The large number of comparisons i ..."
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Cited by 6 (1 self)
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Abstract. In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences amongst n elements of a human subject. The method requires performing all ( n 2 comparisons then sorting elements according to the number of wins. The large number of comparisons is performed to counter the potentially faulty decisionmaking of the human subject, who acts as an imprecise comparator. We consider a simple model of the imprecise comparisons: there exists some δ> 0 such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least δ, then the comparison will be made correctly; when the two elements have values that are within δ, the outcome of the comparison is unpredictable. This δ corresponds to the just noticeable difference unit (JND) or difference threshold in the psychophysics literature, but does not require the statistical assumptions used to define this value. In this model, the standard method of paired comparisons minimizes the errors introduced by the imprecise comparisons at the cost of ( n 2 comparisons. We show that the same optimal guarantees can be achieved using 4n 3/2 comparisons, and we prove the optimality of our method. We then explore the general tradeoff between the guarantees on the error that can be made and number of comparisons for the problems of sorting, maxfinding, and selection. Our results provide closetooptimal solutions for each of these problems. 1
A Lukasiewicz Logic Based Prolog
 Mathware and Soft Computing
, 1994
"... Prolog is a programming language based on a restricted subset of classical first order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a / Lukasiewicz logic based Prolog system. The use of / Lukasiewicz log ..."
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Cited by 4 (1 self)
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Prolog is a programming language based on a restricted subset of classical first order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a / Lukasiewicz logic based Prolog system. The use of / Lukasiewicz logic with its connection to Ulam games enables us to deal with partial inconsistencies by interpreting the truth values as relative distance to contradiction. We also present the software tool LULOG which is based on the theoretical results of this paper and can be seen as a Prolog system for manyvalued logic. Applications of LULOG to an Ulam game and an example of reasoning with imperfect knowledge are also discussed. 1 Introduction Classical logic provides a framework for the formulation and implementation of knowledge based systems. The programming language Prolog [6, 7] is based on a subset of first order predicate logic and thus a considerable number of artificial intelligence applicat...
THE TWOBATCH LIAR GAME OVER AN ARBITRARY CHANNEL ∗
"... Abstract. We consider liar games in which player Paul must ask one full batch of questions, receive all answers, and then ask a second and final batch of questions. We show that the effect of this restriction is asymptotically negligible. The strategy for Paul is given explicitly. ..."
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Cited by 4 (0 self)
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Abstract. We consider liar games in which player Paul must ask one full batch of questions, receive all answers, and then ask a second and final batch of questions. We show that the effect of this restriction is asymptotically negligible. The strategy for Paul is given explicitly.