This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NP-completeness. 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 NP-Completeness,’ ’ 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, cross-references will be given to that book and the list of problems (NP-complete and harder) presented there. Readers who have results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.) or open problems they would like publicized, should

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 yes-or-no 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...

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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challenge, called the file synchronization problem: given two versions of a file on different machines, say an outdated and a current one, how can we update the outdated version with minimum communication cost, by exploiting the significant similarity between the versions?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,

Foraging- and feeding-related behaviors across eumetazoans share similar molecular mechanisms, suggesting the early evolution of an optimal foraging behavior called area-restricted 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 goal-directed behavior and cognition is further supported by pathologies of human goal-directed 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 goal-directed cognition out of mechanisms initially in control of spatial foraging but, through increasing cortical connections, eventually used to forage for information.

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 well-defined 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

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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 many--valued 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...

We study the classic binary search problem, with a delay between query and answer. For all constant delays, we give upper and lower bounds, matching up to an additive constant. 1

Simulation modeling provides a powerful methodology for advancing theory and research on complex behaviors and systems, yet it has been embraced more slowly in management than in some associated social science disciplines. We suspect that part of the reason is that simulation methods are not well understood. We therefore aim to promote understanding of simulation methodology and to develop an appreciation of its potential contributions to management theory by describing the nature of simulations, its attractions, and its special problems, as well as some uses of computational modeling in management research.