This article gives a brief introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other

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

Since the beginning of AI, mind games have been studied as relevant application fields. Nowadays, some programs are better than human players in most classical games. Their results highlight the efficiency of AI methods that are now quite standard. Such methods are very useful to Go programs, but they do not enable a strong Go program to be built. The problems related to Computer Go require new AI problem solving methods. Given the great number of problems and the diversity of possible solutions, Computer Go is an attractive research domain for AI. Prospective methods of programming the game of Go will probably be of interest in other domains as well. The goal of this paper is to present Computer Go by showing the links between existing studies on Computer Go and different AI related domains: evaluation function, heuristic search, machine learning, automatic knowledge generation, mathematical morphology and cognitive science. In addition, this paper describes both the practical aspects of Go programming, such as program optimization, and various theoretical aspects such as combinatorial game theory, mathematical morphology, and MonteCarlo methods. B. Bouzy T. Cazenave page 2 08/06/01 1.

We introduce a new category of finite, fair games, and winning strategies, and use it to provide a semantics for the multiplicative fragment of Linear Logic (mll) in which formulae are interpreted as games, and proofs as winning strategies. This interpretation provides a categorical model of mll which satisfies the property that every (history-free, uniformly) winning strategy is the denotation of a unique cut-free proof net. Abramsky and Jagadeesan first proved a result of this kind and they refer to this property as full completeness. Our result differs from theirs in one important aspect: the mix-rule, which is not part of Girard's Linear Logic, is invalidated in our model. We achieve this sharper characterization by considering fair games. A finite, fair game is specified by the following data: ffl moves which Player can play, ffl moves which Opponent can play, and ffl a collection of finite sequences of maximal (or terminal) positions of the game which are deemed to be fair. N...

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we begin with general background in combinatorial game theory, which analyzes ideal play in perfect-information games. Then we survey results about the complexity of determining ideal play in these games, and the related problems of solving puzzles, in terms of both polynomial-time algorithms and computational intractability results. Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer. 1

Hex is a beautiful game with simple rules and a strategic complexity comparable to that of Chess and Go. The massive game-tree search techniques developed mostly for Chess and successfully used for Checkers and a number of other games, become less useful for games with large branching factors like Hex and Go. In this paper, we describe deduction rules, which are used to calculate values of complex Hex positions recursively starting from the simplest ones. We explain how this approach is implemented in HEXY---the strongest Hex-playing computer program, the Gold medallist of the 5th Computer Olympiad in London, August 2000. 2001 Elsevier Science B.V. All rights reserved.

Abstract. We introduce two equivalent methodologies for defining and computing a position’s mean (value of playing Black rather than White) and temperature (value of next move). Both methodologies apply in more generality than the classical one. The first, following the notion of a free market, relies on the transfer of a “tax ” between players, determined by continuous competitive auctions. The second relies on a generalized thermograph, which reduces to the classical thermograph when the game is loop-free. When a sum of games is played optimally according the economic rules described, the mean (which is additive) and the temperature determine the final score precisely. This framework extends and refines several classical notions. Thus, finite games that are numbers in Conway’s sense are now seen to have negative natural temperatures. All games can now be viewed as terminating naturally with integer scores when the temperature reaches −1.

Abstract. Aim: To present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Ascend from Nim to chess in small strides at a gradient that’s not too steep. Presentation: Informal; examples of games sampled from various strategic viewing points along scenic mountain trails illustrate the theory. 1.

We prove that any countable (finite or infinite) partially ordered set may be represented by nite oriented paths ordered by the existence of homomorphism between them. This (what we believe a surprising result) solves several open problems. Such path-representations were previously known only for finite and infinite partial orders of dimension 2. Path-representation implies the universality of other classes of graphs (such as connected cubic planar graphs). It also implies that finite partially ordered sets are on-line representable by paths and their homomorphisms. This leads to a new on-line dimensions.

A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. The theory of such games is a hybrid between the classical theory of games [von Neumann, Morgenstern, Aumann, . . . ] and the combinatorial theory of games [Berlekamp, Conway, Guy, . . . ]. We expand upon our previous work by considering games with infinitely many positions, and several variants including the Poorman variant in which the high bidder pays the bank (rather than the other player). The algorithmic complexity of our procedure for computing optimal moves is found to be polynomial in several important cases.