
Jos W. H. M. UiterwijkMaastricht University | UM · Department of Data Science and Knowledge Engineering
Jos W. H. M. Uiterwijk
PhD
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178
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Introduction
I am an associate professor at the Department of Data Science and Knowledge Engineering (DKE) of Maastricht University.
My current research interests are solving games and combining Combinatorial Game Theory (CGT) with methods from AI, like alpha-beta.
Additional affiliations
December 1980 - June 1988
July 1988 - present
Publications
Publications (178)
This is Part 2 of three articles on the impact of safe moves on perfectly solving Domineering boards.
In Part 1 (Uiterwijk, 2014b) we provided an exact analysis of 1-step safe moves obtainable in the
very first phase of a Domineering game.
In this part we show that, provided the board is wide or high enough, a player may obtain additional
(multi-s...
In this article we elaborate on the importance of safe moves for perfectly solving Domineering boards. Previously we have defined perfectly solving as "solving without any search", i.e., find-ing a knowledge-based solution. We applied our method to the game of Domineering (cf. Uiterwijk, 2014). A test set of 841 Domineering games, consisting of all...
Combinatorial games are a special category of games sharing the property that the winner is by definition the last player able to move. To solve such games two main methods are being applied. The first is a general NegaScout search with many possible enhancements. This technique is applicable to every game, mainly limited to the size of the game du...
In this paper we describe the perfect solving of rectangular empty Domineering boards. Perfect solving is defined as solving without any search. This is done solely based on the number of various move types in the initial position. For this purpose we first characterize several such move types. Next we define 12 knowledge rules, of increasing compl...
Standard SET is a card game played between any number of players moving simultaneously, where a move means taking a number of cards obeying some predetermined conditions (a Set). It is mainly a game of pattern recognition and speed. The winner is the player obtaining the most Sets.To enable analyzing SET in a more mathematical and game-theoretic se...
As a sequel to an investigation of the standard (partisan) versions of Col and Snort on rectangular boards, we defined impartial versions of both games (dubbed iCol and iSnort). These have the same coloring conditions as their partisan versions, but either player is allowed to use at any move a black or a white stone. For these two games similar st...
In this paper we give an overview of results obtained for solving the combinatorial games of Col and Snort on rectangular boards. For Col on boards with at least one dimension even we give a strategy guaranteeing a win for the second player. For Col on general odd × odd boards we found no applicable strategy, though all experimental data show secon...
In this paper we investigate the game of Konane, using Combinatorial Game Theory and game-specific solving strategies. We focus on narrow rectangular boards ( m × n boards with m ⩽ 4). These are dubbed as Linear Konane, Double Konane, Triple Konane, and Quadruple Konane, respectively. The initial board contains black and white stones in a checkered...
In this paper we investigate the board game Cram, which is an impartial combinatorial game, using an αβ solver. Since Cram is a notoriously hard game in the sense that it is difficult to obtain reliable and useful domain knowledge to use in the search process, we decided to rely on knowledge obtained from Combinatorial Game Theory (CGT). The first...
In this paper we investigate the game of Cram, which is the impartial version of Domineering. We have built Cram endgame databases for all board sizes < 30 squares. We developed a program that fills the databases with their Combinatorial Game Theory (CGT) values. Since Cram is an impartial game, all CGT values for Cram positions are so-called nimbe...
When solving k-in-a-Row games, the Hales-Jewett pairing strategy is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a coverage ratio of 2.0.
When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a coverage ratio of 2.0. In this paper we present a new strategy, called Set Matching. A matching set consists o...
Combinatorial games are a special category of games sharing the property that the winner is by definition the last player able to move. To solve such games two main methods are being applied. The first is a general NegaScout search with many possible enhancements. This technique is applicable to every game, mainly limited by the size of the game du...
We have developed a program called MUDoS (Maastricht University Domineering Solver) that solves Domineering positions in a very efficient way. It enables the solution of known positions (up to the 10 x 10 board) to be much quicker.
More importantly, it enables the solution of 11 x 11 Domineering, a board size that up till now was far out of the rea...
In this paper we present a combinatorial game-theoretic analysis of special Domineering positions. In particular we investigate complex positions that are aggregates of simpler fragments, linked via bridging squares.We build on two theorems that exploit the characteristic of an aggregate of two fragments having as game-theoretic value the sum of th...
We have developed a program called MUDoS (Maastricht University Domineering Solver) that solves Domineering positions in a very efficient way. This enables the solution of known positions so far (up to the 10 x 10 board) much quicker (measured in number of investigated nodes). More importantly, it enables the solution of the 11 x 11 Domineering boa...
This is Part 2 of three articles on the impact of safe moves on perfectly solving Domineering boards. In Part 1 (Uiterwijk, 2014b) we provided an exact analysis of 1-step safe moves obtainable in the very first phase of a Domineering game. In this part we show that, provided the board is wide or high enough, a player may obtain additional (multi-st...
This is the third and final article reporting on the impact of safe moves on perfectly solving Domineering boards. In the previous two articles (Uiterwijk, 2014b, 2014c) we gave an accurate analysis of obtainable safe moves in a Domineering game. Based on the results derived from a test set of all Domineering boards with sizes up to 30, new pattern...
This is Part 2 of three articles on the impact of safe moves on perfectly solving Domineering boards. In Part 1 (Uiterwijk, 2014b) we provided an exact analysis of 1-step safe moves obtainable in the very first phase of a Domineering game. In this part we show that, provided the board is wide or high enough, a player may obtain additional (multi-st...
In this paper we present a combinatorial game-theoretic analysis of special Domineering positions. In particular we investigate complex positions that are aggregates of simpler fragments, linked via bridging squares.
We investigate two theorems that exploit the characteristic of an aggregate of two fragments having as game-theoretic value the sum...
We have constructed endgame databases for all single-component positions up
to 15 squares for Domineering, filled with exact Combinatorial Game Theory
(CGT) values in canonical form. The most important findings are as follows.
First, as an extension of Conway's [8] famous Bridge Splitting Theorem for
Domineering, we state and prove another theorem,...
In this paper we present a combinatorial game-theoretic analysis of special Domineering positions. In particular we investigate complex positions that are aggregates of simpler fragments, linked via bridging squares.
We aim to extend two theorems that exploit the characteristic of an aggregate of two fragments having as game-theoretic value the sum...
This is the third and final article reporting on the impact of safe moves on perfectly solving Domineering boards. In the previous two articles (Uiterwijk, 2014b, 2014c) we gave an accurate analysis of obtainable safe moves in a Domineering game. Based on the results derived from a test set of all Domineering boards with sizes up to 30, new pattern...
Classic methods such as A∗ and IDA∗ are a popular and successful choice for one-player games. However, without an accurate admissible evaluation function, they fail. In this article we investigate whether Monte-Carlo tree search (MCTS) is an interesting alternative for one-player games where A∗ and IDA∗ methods do not perform well. Therefore, we pr...
This article shows how the performance of a Monte-Carlo Tree Search (MCTS) player for Havannah can be improved, by guiding the search in the play-out and selection steps of MCTS. To improve the play-out step of the MCTS algorithm, we used two techniques to direct the simulations, Last-Good-Reply (LGR) and N-grams. Experiments re-veal that LGR gives...
This paper describes the analysis of the game Khet and the implementation of a game engine. Both the state-space complexity and the game-tree complexity of Khet are given. They turn out to be of the same order as those of chess. Based on these results, search techniques are selected that can be used to create an AI player which can play Khet as goo...
This article describes a new, game-independent forward-pruning technique for EXPECTIMAX, called CHANCEPROBCUT. It is the first technique to forward prune in chance nodes. Based on the strong correlation between evaluations obtained from searches at different depths, the technique prunes chance events if the result of the chance node is likely to fa...
In this paper we present results of an investigation of the connection game TwixT. This game has a very large complexity and lacks a good evaluation function based on (human) knowledge. To compensate for these drawbacks we decided to use several mathematical-modelling techniques. These are (1) board dominance based on a Voronoi tesselation, (2) sho...
Monte-Carlo Tree Search (MCTS) is a new best-first search guided by the results of Monte-Carlo simulations. In this article, we introduce two progressive strategies for MCTS, called progressive bias and progressive unpruning. They enable the use of relatively time-expensive heuristic knowledge without speed reduction. Progressive bias directs the s...
Fanorona is the national board game of Madagascar. The game's complexity is approximately the same as that of checkers. In this article, we present a search-based approach for weakly solving this game. It is a well-chosen combination of Proof-Number search and endgame databases. Retrograde analysis is used to generate the endgame databases in which...
Classical methods such as A* and IDA* are a popular and successful choice for one-player games. However, they fail without an accurate admissible evaluation function. In this paper we investigate whether Monte-Carlo Tree Search (MCTS) is an interesting alterna- tive for one-player games where A* and IDA* methods do not perform well. Therefore, we p...
Throughout recent years, Monte-Carlo methods have considerably improved computer Go pro- grams. In particular, Monte-Carlo Tree Search algorithms such as UCT have enabled significant advances in this domain. Phantom Go is a variant of Go which is complicated by the condi- tion of imperfect information. This article compares four Monte-Carlo methods...
Monte-Carlo Tree Search is a new method which has been applied successfully to many games. However, it has never been tested on two-player perfect-information games with a chance factor. Backgam-mon is the reference game of this category. Today's best Backgammon programs are based on reinforcement learning and are stronger than the best human playe...
A família de jogos Mancala oferece boas oportunidades para efectuar nova investigação, tanto no domínio da Matemática como no da Inteligência Artificial. Para ilustrar este facto, iremos apresentar um resumo de resulta-dos há muito conhecidos e de outros mais recentes sobre estes jogos. Embora os investigadores de jogos de tabuleiro possam conhecer...
Only recently. Monte-Carlo Tree Search (MCTS) has substantially contributed to the field of computer Go. So far, in standard MCTS there is only one type of node: every node of the tree represents a single move. Instead of maintaining only this type of node, we propose a second type of node representing groups of moves. Thus, the tree may contain mo...
Das vollständige Manuskript dieser Zuschrift erscheint in: Angew. Chem. Suppl. 1982, 1100. DOI: 10.1002/ange.198211000
In the last decade, proof-number search and Monte-Carlo methods have successfully been applied to the combinatorial-games do- main. Proof-number search is a reliable algorithm. It requires a well defined goal to prove. This can be seen as a disadvantage. In contrast to proof-number search, Monte-Carlo evaluation is a flexible stochastic evaluation...
Dao is an attractive game to play, although it is solvable in a few seconds on a computer. The game is so small that the complete
game graph can be kept in internal memory. At the same time, the number of nodes in the game graph of Dao is large enough
to allow interesting analyses. In the game spectrum, Dao resides between on the one hand trivial g...
In this paper we introduce a new pruning mechanism, called Similarity Pruning for Probabilistic Opponent-Model (PrOM) Search. It is based on imposing a bound on the differences between two or more evaluation
functions. Assuming such a bound exists, we are able to prove two theoretical properties, viz., the bound-conservation property
and the bounde...
In this paper a new method is described for move ordering, called the relative history heuristic. It is a combination of the history heuristic and the butterfly heuristic. Instead of only recording moves which are the best move in a node, we also record the moves which are applied in the search tree. Both scores are taken into account in the relati...
Classical search algorithms rely on the existence of a sufficiently powerful evalua-tion function for non-terminal states. In many task domains, the development of such an evaluation function requires substantial effort and domain knowledge, or is not even possible. As an alternative in recent years, Monte-Carlo evaluation has been succesfully appl...
The game of Go is one of the games that still withstand classical Articial Intelligence approaches. Hence, it is a good testbed for new AI methods. Amongst them, Monte-Carlo led to promising results. This method consists of building an evaluation function by averaging the outcome of several randomized games. The paper introduces a new strategy, whi...
Over the years, proof-number search has successfully been applied to many game domains. This article proposes two new pattern-based heuristics for move ordering in proof-number search. One heuristic applies patterns directly, the other heuristic uses patterns to control Monte-Carlo sampling. The test domain is the Life-and-Death problem in the game...
This article investigates the application of machine-learning techniques for the task of scoring final positions in the game of Go. Neural network classifiers are trained to classify life and death from labelled 9×9 game records. The performance is compared to standard classifiers from statistical pattern recognition. A recursive framework for clas...
Opponent-Model search is a game-tree search method that explicitly uses knowledge of the opponent. There is some risk involved in using Opponent-Model search. For adequate forecasting, two conditions should be imposed. Both the prediction of the opponent's moves and the judgement of future positions should be of good quality. The two conditions hea...
In this paper forward-pruning methods, such as multi-cut and null move, are tested at so-called ALL nodes. We improved the principal variation search by four small but essential additions. The new PVS algorithm guarantees that forward pruning is safe at ALL nodes. Experiments show that multi-cut at ALL nodes (MC-A) when combined with other forward-...
This article presents a new learning system for predicting life and death in the game of Go. It is called Gone. The system uses a multi-layer perceptron classifier which is trained on learning examples extracted from game records. Blocks of stones are represented by a large amount of features which enable a rather precise prediction of life and dea...
In Probabilistic Opponent-Model search (PrOM search) the opponent is modelled by a mixed strategy of N opponent types ω
0 ... ω
N − − 1. The opponent is assumed to adopt at every move one of the opponent types ω
i
according to the probability Pr(ω
i
). We hypothesize that PrOM search is a better search mechanism than Opponent-Model search (OM searc...
This paper investigates methods for estimating potential territory in the game of Go. We have tested the performance of direct
methods known from the literature, which do not require a notion of life and death. Several enhancements are introduced which
can improve the performance of the direct methods. New trainable methods are presented for learni...
The paper presents a new proof-number (PN) search algorithm, called PDS–PN. It is a two-level search (like PN2), which performs at the first level a depth-first proof-number and disproof-number search (PDS), and at the second level a best-first PN search. Hence, PDS–PN selectively exploits the power of both PN2 and PDS. Experiments in the domain of...
This article presents a search-based approach of solving Go on small boards. A dedicated heuristic evaluation function combined with the static recognition of unconditional territory is used in an alpha-beta framework with several domain-dependent and domain-independent search enhancements. We present two variants of the GHI problem (caused by supe...
Lines of Action (LOA) is a two-person zero-sum chess-like connection game. Building an evaluation function for LOA is a difficult task because not much knowledge about the game is available. In this paper the evaluation function of the tournament program MIA is explained. This evaluator consists of the following nine features: concentration, centra...
This paper investigates the application of the the killer-tree heuristic (KTH) and the λ1-search method to the endgame of lines of action. Both techniques are developed to be used in the endgame of shogi. They are incorporated into two depth-first searches: iterative deepening αβ and PDS. λ1-Search, in which the move generation is limited to λ1-mov...
The article investigates two learning algorithms for forward pruning. The TS-FPV algorithm uses a tabu-search (TS) algorithm to explore the space of the forward-pruning vectors (FPVs). It focuses on critical FPVs. The RL-FPF algorithm is a reinforcement-learning (RL) algorithm for forward-pruning functions (FPFs). It uses a gradient-descent update...
Opponent-model (OM) search comes with two types of risk. The first type is caused by a playerÕs imperfect knowledge of the opponent, the second type arises from low-quality evaluation functions. In this paper, we investigate the desirability of a precon-dition, called admissibility, that may prevent the second type of risk. We examine the results o...
Using full-game databases and optimized tree-search algorithms, the game of Kalah is solved for several starting configurations up to 6 holes and 5 counters per hole. The main search algorithm used was iterative-deepening MTD(f). Major search enhancements were move ordering, transposition tables, futility pruning, enhanced transposition cut-off, an...
Opponent-Model search is a game-tree search method that explicitly uses knowl- edge of the opponent. There is some risk involved in using Opponent-Model search. Both the prediction of the opponent's moves and the estimation of the profitability of future positions should be of good quality and as such they should obey certain conditions. To investi...
Abstract,This paper presents a learning system for scoring final positions in the Game of Go. Our system learns to predict life and death from labelled game,records. 98.9% of the positions are scored correctly and nearly all incorrectly scored positions are recognized. By providing reliable score information our system opens the large source of Go...
Lines of Action (LOA) is a two-person zero-sum chess-like connection game. Building an evaluation function for LOA is a difficult task be cause not much knowledge about the game is available. In this paper the evaluation function of the tournament program MIA is explained. This evaluator consists of the following nine features: concentration, centr...
The paper introduces a new proof-number (PN) search algorithm, called PDS-PN. It is a two-level search, which performs at the first level a depth-first Proof-number and Disproof-number Search (PDS), and at the second level a best-first PN search. First, we thoroughly investigate four established algorithms in the domain of Lines of Action endgame p...
The family of mancala games offers opportunities for new research in both Mathematics and Artificial Intelligence. To illustrate this, we will present an overview of long-time known and more recent results on mancala games. Although board-games researchers may be familiar with mancala games, the general properties of this family of board games will...
The paper introduces a new proof-number (PN) search algorithm, called PDS-PN. It is a two-level search, which performs at the first level a depth-first Proof-number and Disproof-number Search (PDS), and at the second level a best-first PN search. First, we thoroughly investigate four, established algorithms in the domain of Lines of Action endgame...
This paper investigates to what extent learning methods are beneficial for the Lines of Action tournament program MIA. We focus on two components of the program: (1) the evaluation function and (2) the move ordering.
This paper investigates to what extent learning methods are beneficial for the Lines of Action tournament program MIA. We focus on two components of the program: (1) the evaluation function and (2) the move ordering. Using temporal difference learning the evaluation function was improved by tuning the weights. We found substantial improvements for...
This paper investigates to what extent learning methods are beneficial for
the Lines of Action tournament program MIA. We focus on two components
of the program: (1) the evaluation function and (2) the move ordering.
Using temporal difference learning the evaluation function was improved by
tuning the weights. We found substantial improvements for...
The paper presents a system that learns to predict local strong expert moves in the game of Go at a level comparable to that of strong human kyu players. This performance is achieved by four techniques. First, our training algorithm is based on a relativetarget approach that avoids needless weight adaptations characteristic of most neural-network c...
The efficiency of alpha-beta search algorithms heavily depends on the order in which the moves are examined. This paper investigates
a new move-ordering heuristic in chess, namely the Neural MoveMap (NMM) heuristic. The heuristic uses a neural network to
estimate the likelihood of a move being the best in a certain position. The moves considered mo...
In this article we present an overview on the state of the art in games solved in the domain of two-person zero-sum games with perfect information. The results are summarized and some predictions for the near future are given. The aim of the article is to determine which game characteristics are predominant when the solution of a game is the main t...
This paper presents a search-based approach for the game of PonnukiGo.
A thorough analysis of OM search reveals an important deficiency that has not been detected so far. It turns out that applying OM search is dangerous when the own evaluation function is not perfect, in particular when it overestimates the value of a position that the opponent does not overestimate. Such a position then acts as an attractor to which...
The mancala games Awari and Kalah have been studied in Artificial Intelligence research for a long time. After the recent solving of Kalah and, only very recently, Awari, the time has come to consider other, more complex, mancala games. Within the large group of mancala games, Zanzibar Bao is considered the most complex one. In this paper, we give...
This paper proposes a new Eye-based Recurrent Network Architecture (ERNA) for image classification. The new architecture is trained by a combination of Qlearning and RPROP. The classification performance is compared with other network architectures on the task of determining connectedness between pixels in small binary images. The experiments show...
A new approach for heuristic game-tree search, probabilistic opponent-model search (PrOM search), is proposed. It is based on standard opponent-model search (OM search). The new approach takes into account a multiple-opponent model. It incorporates uncertainty which mimics the uncertainty of a player about the behaviour of the opponent. Some theore...
The efficiency of alpha-beta search algorithms heavily de- pends on the order in which the moves are examined. This paper
focuses on using neural networks to estimate the likelihood of a move being the best in a certain position. The moves considered
more likely to be the best are examined first. We selected Lines of Action as a testing ground. We...
This paper proposes a new search algorithm, denoted PN∗, for AND/OR tree search. The algorithm
is based on proof-number (PN) search, a best-first search algorithm, proposed by Allis et al.
[Artificial Intelligence 66 (1) (1994) 91–124], and on Korf’s RBFS algorithm [Artificial Intelligence
62 (1) (1993) 41–78]. PN∗ combines several existing ideas....
Lines of Action (LOA) is a two-person zero-sum chess-like connection game with perfect information. The goal of each side is to connect its own pieces. The state-space complexity and game-tree complexity are comparable with those of Othello. A LOA evaluation function usually consists of a combination of the following components: threats, solid form...
In this contribution we propose a class of strategies which focus on the game as well as on the opponent. Preference is given to the thoughts of the opponent, so that the strategy under investigation might be speculative. We describe a generalization of OM search, called (D,d)-OM search, where D stands for the depth of search by the player and d fo...
Best-first search algorithms usually amalgamate identical nodes for optimization reasons, meanwhile transforming the search tree into a search graph. However, identical nodes may represent different search states, e.g., due to a difference of history. So, in a search graph a node's value may be dependent on the path leading to it. This implies that...
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