Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to $n \times n$ board (for natural $n$ greater than $3$). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs

On the Impact of Information Technologies on Society: an Historical Perspective through the Game of Chess

The game of chess as always been viewed as an iconic representation of intellectual prowess. Since the very beginning of computer science, the challenge of being able to program a computer capable of playing chess and beating humans has been alive and used both as a mark to measure hardware/software progresses and as an ongoing programming challenge leading to numerous discoveries. In the early days of computer science it was a topic for specialists. But as computers were democratized, and the strength of chess engines began to increase, chess players started to appropriate to themselves these new tools. We show how these interactions between the world of chess and information technologies have been herald of broader social impacts of information technologies. The game of chess, and more broadly the world of chess (chess players, literature, computer softwares and websites dedicated to chess, etc.), turns out to be a surprisingly and particularly sharp indicator of the changes induced in our everyday life by the information technologies. Moreover, in the same way that chess is a modelization of war that captures the raw features of strategic thinking, chess world can be seen as small society making the study of the information technologies impact easier to analyze and to grasp

The role of structured induction in expert systems

A "structured induction" technique was developed and tested using a rules- from -examples generator together with a chess -specific application package. A drawback of past experience with computer induction, reviewed in this thesis, has been the generation of machine -oriented rules opaque to the user. By use of the structured approach humanly understandable rules were synthesized from expert supplied examples. These rules correctly performed chess endgame classifications of sufficient complexity to be regarded as difficult by international master standard players. Using the "Interactive ID3" induction tools developed by the author, chess experts, with a little programming support, were able to generate rules which solve problems considered difficult or impossible by conventional programming techniques. Structured induction and associated programming tools were evaluated using the chess endgames Icing and Pawn vs. King (Black -tomove) and King and Pawn vs. King and Rook (White -to -move, White Pawn on a7) as trial problems of measurable complexity.Structured solutions to both trial problems are presented, and implications of this work for the design of expert systems languages are assessed

Validation of machine-oriented strategies in chess endgames

This thesis is concerned with the validation of chess endgame strategies. It is also concerned with the synthesis of strategies that can be validated. A strategy for a given player is the specification of the move to be made by that player from any position that may occur. This move may be dependent on the previous moves of both sides. A strategy is said to be correct if following the strategy always leads to an outcome of at least the same game theoretic value as the starting position. We are not concerned with proving the correctness of programs that implement the strategies under consideration. We shall be working with knowledge-based programs which produce playing strategies, and assume that their concrete implementations (in POP2, PROLOG etc.) are correct. The synthesis approach taken attempts to use the large body of heuristic knowledge and theory, accumulated over the centuries by chessmasters, to find playing strategies. Our concern here is to produce structures for representing a chessmaster's knowledge wnich can be analysed within a game theoretic model. The validation approach taken is that a theory of the domain in the form of the game theoretic model of chess provides an objective measure of the strategy followed by a program. Our concern here is to analyse the structures created in the synthesis phase. This is an instance of a general problem, that of quantifying the performance of computing systems. In general to quantify the performance of a system we need,- A theory of the domain. - A specification of the problem to be solved. - Algorithms and/or domain-specific knowledge to be applied to solve the problem

A novel computer Scrabble engine based on probability that performs at championship leve

The thesis starts by giving an introduction to the game of Scrabble, then mentions state-of-the-art computer Scrabble programs and presents some characteristics of our developed Scrabble engine Heuri. Some brief notions of Game Theory are given, along with history of some games in Artificial Intelligence; the fundamental algorithms for game playing, as well as state-of-the-art engines and the algorithms used by them, are presented. Basic elements of Scrabble, such as the Scrabble rules and the letter distribution, are given. Some history and state-of-the-art of Computer Scrabble are commented. For instance, the generation methods of valid moves based on the data structure DAWG (Directed Acyclic Word Graph) and also the variant GADDAG are recalled. These methods are used by the state-of-the-art Scrabble engines Quackle and Maven. Then, the contributions of this thesis are presented. A Spanish lexicon for playing Scrabble has been built that is used by Heuri engines. From this construction, a detailed study and classification of Spanish irregular verbs has been provided. A novel Scrabble move generator based on anagrams has been designed and implemented, which has been shown to be faster than the GADDAG-based generator used in Quackle engine. This method is similar to the way Scrabble players look for a move, searching for anagrams and a spot to play on the board. Next, we address the evaluation of moves when playing Scrabble; the quality of your game depends on deciding what move should be played given a certain board and a rack with tiles. This decision was made initially by Heuri trying several heuristics which ended up with the construction of several engines. We give the explanation of the heuristics used in these engines, all of them based on probabilities. All these initial heuristic evaluation functions (up to six) do not use forward looking, they are static evaluators. They have shown, after testing, an increasing playing performance, which allow Heuri to beat (top-level) expert human players in Spanish, without the need of using sampling and simulation techniques. These heuristics mainly consider the possibility of achieving a bingo on the actual board, whereas Quackle used pre-calculated values (superleaves) regardless of the latter. Then, in order to improve the quality of play of Heuri even more, some additional engines are presented in which look ahead is employed. The HeuriSamp engine, which evaluates a 2-ply search, permits to obtain a defense value. The HeuriSim engine uses a 3-ply adversarial search tree; it contemplates the best first moves (according to Heuri sixth engine heuristic) from Player 1, then some replies to these moves (Player 2 moves) and then some replies to these replies (Player 1 moves). Finally, to improve these engines, opponent modeling is used; this technique makes predictions on some of the opponents' tiles based on the last play made by the opponent. We present results obtained by playing thousands of Heuri vs Heuri games, collecting important information: general statistics of Scrabble game, like a 16 point handicap of the second player, and word statistics in Spanish, like a list of the most frequently played bingos (words that use all 7 tiles of a player's rack). In addition, we present results of matches played by Heuri against top-level humans in Spanish and results obtained by massive playing of different Heuri engines against the Quackle engine in Spanish, French and English. All these match results demonstrate the championship level performance of the Heuri engines in the three languages, especially of the last developed engine that includes simulation and opponent modeling techniques. From here, conclusions of the thesis are drawn and work for the future is envisaged.La tesi comença introduint el joc del Scrabble, esmentant els programes d’ordinador de l’estat de l’art que juguen Scrabble, i presentant algunes característiques del motor de joc de Scrabble que s’ha desenvolupat anomenat Heuri. Es donen breus nocions de la Teoria de Jocs, junt amb la història d’alguns jocs en Intel·ligència Artificial; es presenten els algorismes fonamentals per jugar, així com els motors de joc de l’estat de l’art en diferents jocs i els algorismes que usen. Es comenta també la història i estat de l’art del Computer Scrabble. Es recorden els mètodes de generació de moviments vàlids basats en l’estructura de dades DAWG (Directed Acyclic Word Graph) i en la variant GADDAG, que són usats pels motors de joc de Scrabble Quackle i Maven. A continuació es presenten les contribucions de la tesi. S’ha construït un diccionari per jugar Scrabble en espanyol, el qual és usat per les diferentes versions del motor de joc Heuri. S’ha fet un estudi detallat i una classificació dels verbs irregulars en espanyol. S’ha dissenyat i implementat un nou generador de moviments de Scrabble basat en anagrames, que ha demostrat ser més ràpid que el generador basat en GADDAG usat al motor Quackle. Aquest mètode és similar a la manera en la que els jugadors de Scrabble cerquen un moviment, buscant anagrames i un lloc del tauler on col·locar-los. Seguidament, es tracta l’evacuació dels moviments quan es juga Scrabble; la qualitat del joc depèn de decidir quin moviment cal jugar donat un cert tauler i un faristol amb fitxes. En Heuri, inicialment, aquesta decisió es va prendre provant diferents heurístiques que van dur a la construcció de diversos motors. Donem l’explicació de les heurístiques usades en aquests motors, totes elles basades en probabilitats. Totes aquestes funcions d’avaluació heurística inicials (fins a sis) no miren cap endavant, fan avaluacions estàtiques. Han mostrat, després de ser provades, un rendiment creixent de nivell de joc, el que ha permès Heuri derrotar a jugadors humans experts de màxim nivell en espanyol, sense necessitat d’usar tècniques de mostreig i de simulació. Aquestes heurístiques consideren principalment la possibilitat d’aconseguir un bingo en el tauler actual, mentre que Quackle usa uns valors pre-calculats (superleaves) que no tenen en compte l’anterior. Amb l’objectiu de millorar la qualitat de joc de Heuri encara més, es presenten uns motors de joc addicionals que sí miren cap endavant. El motor HeuriSamp, que realitza una cerca 2-ply, permet obtenir un valor de defensa. El motor HeuriSim usa un arbre de cerca 3-ply; contempla els millors primers moviments (d’acord al sisè motor heurístic d’Heuri) del Jugador 1, després algunes respostes a aquests moviments (moviments del Jugador 2) i llavors algunes rèpliques a aquestes respostes (moviments del Jugador 1). Finalment, per a millorar aquests motors, es proposa usar modelatge d’oponents; aquesta tècnica realitza prediccions d’algunes de les fitxes de l’oponent basant-se en l’últim moviment jugat per aquest. Es presenten resultats obtinguts de jugar milers de partides d’Heuri contra Heuri, que recullen important informació: estadístiques generals del joc del Scrabble, com un handicap de 16 punts del segon jugador, i estadístiques de paraules en espanyol, com una llista dels bingos (paraules que usen les 7 fitxes del faristol d’un jugador) que es juguen més freqüentment. A més, es presenten resultats de partides jugades per Heuri contra jugadors humans de màxim nivell en espanyol i resultats obtinguts d'un gran nombre d’enfrontaments entre els diferents motors de joc d’Heuri contra el motor Quackle en espanyol, francès i anglès. Tots aquests resultats de partides jugades demostren el rendiment de nivell de campió dels motors d’Heuri en les tres llengües, especialment el de l’últim motor desenvolupat que inclou tècniques de de simulació i modelatge d'oponents. A partir d'aquí s'extreuen les conclusions de la tesi i es preveu treballar de cara al futur.Postprint (published version

An Experimental Study on Young Pupils

Chess is thought to be a game demanding high cognitive abilities to be played well. Although many studies proved the link between mastery in chess and high degree of intelligence, just few studies proved that chess practice can enhance cognitive abilities. Starting from these considerations, the main purpose of the present research was to investigate the potential benefits of in-presence chess lessons and on-line training on mathematical problem-solving ability in young pupils (8 to 11 years old). Five hundred sixty students were divided into two groups, experimental (which had chess course and on-line training) and control (which had normal school activities), and tested on their mathematical and chess abilities. Results show a strong correlation between chess and math scores, and a higher improvement in math in the experimental group compared with the control group. These results foster the hypothesis that even a short-time practice of chess in children can be a useful tool to enhance their mathematical abilities

On the Impact of Information Technologies on Society: an Historical Perspective through the Game of Chess

12 pages - ISSN: 2105-0422The game of chess has always been viewed as an iconic representation of intellectual prowess. Since the very beginning of computer science, the challenge of being able to program a computer to play chess, and to beat humans, has been alive and has been used both as a mark to measure hardware/software progresses and as an ongoing programming challenge leading to numerous discoveries. In the early days of computer science it was an affair of specialists. But as computers were democratized, and the strength of chess engines started to increase, chess players started to appropriate to themselves these new tools. We show how these interactions between the world of chess and information technologies have been herald of broader social impacts of information technologies. The game of chess, and more broadly the world of chess (chess players, literature, computer softwares and website dedicated to chess, etc.), turns out to be a surprisingly and particularly sharp indicator of the changes induced in our every day life by the information technologies. Moreover in the same way that chess is a modelization of war that captures the raw features of strategic thinking, chess world can be seen as small society making the study of the information technologies impact easier to analyse and to grasp

The 1990 progress report and future plans

This document describes the progress and plans of the Artificial Intelligence Research Branch (RIA) at ARC in 1990. Activities span a range from basic scientific research to engineering development and to fielded NASA applications, particularly those applications that are enabled by basic research carried out at RIA. Work is conducted in-house and through collaborative partners in academia and industry. Our major focus is on a limited number of research themes with a dual commitment to technical excellence and proven applicability to NASA short, medium, and long-term problems. RIA acts as the Agency's lead organization for research aspects of artificial intelligence, working closely with a second research laboratory at JPL and AI applications groups at all NASA centers