. The use of a lower bound estimate in the search has a tremendous impact on the size of the resulting search trees, whereas OBDDs can be used to efficiently describe sets of states based on their binary encoding. This paper combines these two ideas into a new algorithm BDDA . It challenges both the breadth-first search using OBDDs and the traditional A algorithm. The problem with A is that in many application areas the set of states is too huge to be kept in main memory. In contrast, brute-force breadth-first search using OBDDs unnecessarily expands several nodes. Therefore, we exhibit a new trade-off between time and space requirements and tackle the most important problem in heuristic search, the overcoming of space limitations while avoiding a strong penalty in time. We evaluate our approach in the (n 2 \Gamma 1)-Puzzle and within Sokoban. 1 Introduction In heuristic search we explore the state space by generating the successor set over and over again. The choice...

Computer Go is one of the biggest challenges faced by game programmers. This survey describes the typical components of a Go program, and discusses knowledge representation, search methods and techniques for solving specific subproblems in this domain. Along with a summary of the

this paper a simple classification of several known algorithms for finding the maxima, together with several new algorithms; among these are two efficient algorithms---one with expected complexity n +O( # nlogn) when the point samples are issued from some planar regions, and another more efficient than existing ones

ABSTRACT 2 This paper intends to provide an analytical overview of the research performed in the domain of computer Go. Domain knowledge that is essential to Go-playing programs is identified. Various computation and search techniques that can be used effectively to obtain helpful domain knowledge are presented. Four different move-decision paradigms applied by today’s leading Go programs are discussed. Conclusions are drawn and two proposals of improvements to current move-decision paradigms are presented. 1.

Position evaluation is a critical component of Go programs. This paper describes both the exact and the heuristic methods for position evaluation that are used in the Go program Explorer, and outlines some requirements for developing better Go evaluation functions in the future. 1

Abstract. Alpha-beta pruning is the algorithm of choice for searching game trees with position values taken from a totally ordered set, such as the set of real numbers. We generalize to game trees with position values taken from a partially ordered set, and prove necessary and sufficient conditions for alpha-beta pruning to be valid. Specifically, we show that shallow pruning is possible if and only if the value set is a lattice, and full alphabeta pruning is possible if and only if the value set is a distributive lattice. We show that the resulting technique leads to substantial improvements in the speed of algorithms dealing with card play in contract bridge. 1.

Capturing races or semeai are an important element of Go strategy and tactics. We extend previous work on semeai [1] by introducing a more general framework for analyzing semeai, based on the new concepts of conditional combinatorial games and liberty count games. We show how this framework encompasses earlier concepts such as plain liberty regions and plain eye regions. Furthermore, we discuss how to use upper and lower bounds on such games in a semeai solver. 1 Capturing Races in Go Figure 1: Two simple semeai A semeai in the game of Go can be defined informally as “a race to capture between two adjacent groups that cannot both live”. Figure 1 shows two simple cases. In earlier work [1, 2], we gave more formal definitions of semeai, and described nine different classes of semeai. Semeai of classes 0, 1 and 2 can be detected and evaluated statically, without search. The other classes cover semeai that can be resolved by search, potential semeai, and unclear situations which might end up as a race to capture. This paper contains the following contributions: 1. Section 2 develops a general framework for analyzing semeai in terms of conditional combinatorial games and liberty count games. This framework provides a new basis for the previous model introduced in [1] that used eye and liberty regions. 2. Section 3 extends the semeai analysis framework for cases where an exact game may be difficult to compute, but an easier to obtain upper or lower bound can lead to a resolution of the semeai problem. We only seek to determine the win/loss/seki outcome of a semeai. We do not consider other issues here, such as maximizing the score, computing the combinatorial game value, or determining whether winning a semeai is beneficial at all [1]. In the remainder of this paper we will use the following terms that were defined in [1]: Essential and nonessential block, outside liberty, plain outside liberty, shared liberty, eye, plain eye, nakade, class semeai.

Games are a popular test bed for AI research. Many of the search techniques that are currently used in areas such as single-agent search and AI planning have been originally developed for games such as chess. Games share one fundamental problem with many other fields such as AI planning or operations research: how to evaluate and compare complex states? The classical approach is to ‘boil down ’ state evaluation to a single scalar value. However, a single value is often not rich enough to allow meaningful comparisons between states, and to efficiently control a search. In the context of games research, a number of search methods using multicriteria evaluation have been developed in recent years. This paper surveys these approaches, and outlines a possible joint research agenda for the fields of AI planning and game-playing in the domain of multicriteria evaluation.