A Case Study of a Chess Conjecture
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Multilinear Algebra and Chess Endgames
Games of No Chance MSRI Publications Volume 29, 1996 Multilinear Algebra and Chess Endgames LEWIS STILLER Abstract. This article has three chief aims: (1) To show the wide utility of multilinear algebraic formalism for high-performance computing. (2) To describe an application of this formalism in the analysis of chess endgames, and results obtained thereby that would have been impossible to compute using earlier techniques, including a win requiring a record 243 moves. (3) To contribute to the study of the history of chess endgames, by focusing on the work of Friedrich Amelung (in particular his apparently lost analysis of certain six-piece endgames) and that of Theodor Molien, one of the founders of modern group representation theory and the first person to have systematically numerically analyzed a pawnless endgame. 1. Introduction Parallel and vector architectures can achieve high peak bandwidth, but it can be difficult for the programmer to design algorithms that exploit this bandwidth efficiently. Application performance can depend heavily on unique architecture features that complicate the design of portable code [Szymanski et al. 1994; Stone 1993]. The work reported here is part of a project to explore the extent to which the techniques of multilinear algebra can be used to simplify the design of high- performance parallel and vector algorithms [Johnson et al. 1991]. The approach is this: Define a set of fixed, structured matrices that encode architectural primitives • of the machine, in the sense that left-multiplication of a vector by this matrix is efficient on the target architecture. Formulate the application problem as a matrix multiplication. -
Yale Yechiel N. Robinson, Patent Attorney Email: [email protected]
December 16, 2019 From: Yale Yechiel N. Robinson, Patent Attorney Email: [email protected] To: United States Patent and Trademark Office (USPTO) Email: [email protected] Re: Request for Comments on Intellectual Property Protection for Artificial Intelligence Innovation, Docket number: PTO-C-2019-0038 To the USPTO and Members of the Public: My name is Yale Robinson. In addition to my professional work as a patent attorney and in other legal matters, I have for years enjoyed the intergenerational conversation within the game of chess, which originated many centuries ago and spread across Europe and North America around the middle of the 19th century, and has since reached every major country in the world. I will direct my comments regarding issues of intellectual property for artificial intelligence innovations based on the history of traditional western chess. Early innovators in computing, including Alan Turing and Claude Shannon, tried to calculate the value of certain chess positions using the 1950-era equivalent of a present-day handheld calculator. Their work launched the age of computer chess, where the strongest present-day computers can consistently (but not always) defeat or draw elite human grandmasters. The quality of human-versus-human play has increased in part because of computer analysis of opening and middle-game positions that strong players can analyze and practice playing on their home computer device before trying the idea against a human player in competition. In addition to the development of chess theory for the benefit of chess players (human and electronic alike), the impact of chess computing has arguably extended beyond the limits of the game itself. -
PUBLIC SUBMISSION Status: Pending Post Tracking No
As of: January 02, 2020 Received: December 20, 2019 PUBLIC SUBMISSION Status: Pending_Post Tracking No. 1k3-9dz4-mt2u Comments Due: January 10, 2020 Submission Type: Web Docket: PTO-C-2019-0038 Request for Comments on Intellectual Property Protection for Artificial Intelligence Innovation Comment On: PTO-C-2019-0038-0002 Intellectual Property Protection for Artificial Intelligence Innovation Document: PTO-C-2019-0038-DRAFT-0009 Comment on FR Doc # 2019-26104 Submitter Information Name: Yale Robinson Address: 505 Pleasant Street Apartment 103 Malden, MA, 02148 Email: [email protected] General Comment In the attached PDF document, I describe the history of chess puzzle composition with a focus on three intellectual property issues that determine whether a chess composition is considered eligible for publication in a magazine or tournament award: (1) having one unique solution; (2) not being anticipated, and (3) not being submitted simultaneously for two different publications. The process of composing a chess endgame study using computer analysis tools, including endgame tablebases, is cited as an example of the partnership between an AI device and a human creator. I conclude with a suggestion to distinguish creative value from financial profit in evaluating IP issues in AI inventions, based on the fact that most chess puzzle composers follow IP conventions despite lacking any expectation of financial profit. Attachments Letter to USPTO on AI and Chess Puzzle Composition 35 - Robinson second submission - PTO-C-2019-0038-DRAFT-0009.html[3/11/2020 9:29:01 PM] December 20, 2019 From: Yale Yechiel N. Robinson, Esq. 505 Pleasant Street #103 Malden, MA 02148 Email: [email protected] To: Andrei Iancu Director of the U.S. -
Shredder User Manual
Shredder User Manual Shredder User Manual ........................................................................................................................1 Shredder by Stefan Meyer•Kahlen ......................................................................................................4 Note ................................................................................................................................................4 Registration.....................................................................................................................................4 Contact ...........................................................................................................................................5 Stefan Meyer•Kahlen.......................................................................................................................5 Using Shredder...................................................................................................................................6 Menus .............................................................................................................................................6 File Menu.....................................................................................................................................6 Commands Menu.........................................................................................................................8 Levels Menu ................................................................................................................................9 -
Glossary of Chess
Glossary of chess See also: Glossary of chess problems, Index of chess • X articles and Outline of chess • This page explains commonly used terms in chess in al- • Z phabetical order. Some of these have their own pages, • References like fork and pin. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific to chess problems, see Glossary of chess problems; for a list of chess-related games, see Chess variants. 1 A Contents : absolute pin A pin against the king is called absolute since the pinned piece cannot legally move (as mov- ing it would expose the king to check). Cf. relative • A pin. • B active 1. Describes a piece that controls a number of • C squares, or a piece that has a number of squares available for its next move. • D 2. An “active defense” is a defense employing threat(s) • E or counterattack(s). Antonym: passive. • F • G • H • I • J • K • L • M • N • O • P Envelope used for the adjournment of a match game Efim Geller • Q vs. Bent Larsen, Copenhagen 1966 • R adjournment Suspension of a chess game with the in- • S tention to finish it later. It was once very common in high-level competition, often occurring soon af- • T ter the first time control, but the practice has been • U abandoned due to the advent of computer analysis. See sealed move. • V adjudication Decision by a strong chess player (the ad- • W judicator) on the outcome of an unfinished game. 1 2 2 B This practice is now uncommon in over-the-board are often pawn moves; since pawns cannot move events, but does happen in online chess when one backwards to return to squares they have left, their player refuses to continue after an adjournment. -
Chess Problem Composing Steps
Appendix A Chess Problem Composing Steps Chess problems for this research were composed automatically using CHESTHETICA (see Fig. A.1) following the essential steps below. It is a modi- fication of the approach used in (Iqbal 2011). The problems composed are limited to orthodox mate-in-3 problems in standard international chess. 1. Obtain the two new DSNS strings produced from the DSNS process (see Sect. 3.1). 2. Set the total number of white pieces and black pieces that can be used in the composition. There are two attribute values pertaining to these features in each DSNS string. (a) For example, if in string 1 the white piece count is 5 and in string 2 the white piece count is 10, the range possible for this computer composition is between 5 and 10. The same for the black pieces. 3. Calculate the total Shannon value of the white pieces and then the black pieces in both strings and get the average of each. Use these average values to determine the number of piece permutations (i.e. combinations of different pieces) that satisfy them. (a) For example, an average value of 10 for white could mean having a bishop, two knights and a pawn whereas an average value of 9 for black could mean having just a queen. The total number of piece permutations possible for both the white and black pieces here is totaled. (b) This total will equal the number of times the same pair of DSNS strings is used in attempting to generate a composition. So, in principle, every legal piece combination can be tested. -
Python-Chess Release 0.23.6
python-chess Release 0.23.6 May 25, 2018 Contents 1 Introduction 3 2 Documentation 5 3 Features 7 4 Installing 13 5 Selected use cases 15 6 Acknowledgements 17 7 License 19 8 Contents 21 8.1 Core................................................... 21 8.2 PGN parsing and writing......................................... 34 8.3 Polyglot opening book reading...................................... 41 8.4 Gaviota endgame tablebase probing................................... 43 8.5 Syzygy endgame tablebase probing................................... 44 8.6 UCI engine communication....................................... 46 8.7 SVG rendering.............................................. 53 8.8 Variants.................................................. 54 8.9 Changelog for python-chess....................................... 56 9 Indices and tables 77 i ii python-chess, Release 0.23.6 Contents 1 python-chess, Release 0.23.6 2 Contents CHAPTER 1 Introduction python-chess is a pure Python chess library with move generation, move validation and support for common formats. This is the Scholar’s mate in python-chess: >>> import chess >>> board= chess.Board() >>> board.legal_moves <LegalMoveGenerator at ... (Nh3, Nf3, Nc3, Na3, h3, g3, f3, e3, d3, c3, ...)> >>> chess.Move.from_uci("a8a1") in board.legal_moves False >>> board.push_san("e4") Move.from_uci('e2e4') >>> board.push_san("e5") Move.from_uci('e7e5') >>> board.push_san("Qh5") Move.from_uci('d1h5') >>> board.push_san("Nc6") Move.from_uci('b8c6') >>> board.push_san("Bc4") Move.from_uci('f1c4') >>> board.push_san("Nf6") Move.from_uci('g8f6') >>> board.push_san("Qxf7") Move.from_uci('h5f7') >>> board.is_checkmate() True >>> board Board('r1bqkb1r/pppp1Qpp/2n2n2/4p3/2B1P3/8/PPPP1PPP/RNB1K1NR b KQkq - 0 4') 3 python-chess, Release 0.23.6 4 Chapter 1. Introduction CHAPTER 2 Documentation • Core • PGN parsing and writing • Polyglot opening book reading • Gaviota endgame tablebase probing • Syzygy endgame tablebase probing • UCI engine communication • Variants • Changelog 5 python-chess, Release 0.23.6 6 Chapter 2. -
A Complete Chess Engine Parallelized Using Lazy SMP
A Complete Chess Engine Parallelized Using Lazy SMP Emil Fredrik Østensen Thesis submitted for the degree of Master in programming and networks 60 credits Department of informatics Faculty of mathematics and natural sciences UNIVERSITY OF OSLO Autumn 2016 A Complete Chess Engine Parallelized Using Lazy SMP Emil Fredrik Østensen © 2016 Emil Fredrik Østensen A Complete Chess Engine Parallelized Using Lazy SMP http://www.duo.uio.no/ Printed: Reprosentralen, University of Oslo Abstract The aim of the thesis was to build a complete chess engine and parallelize it using the lazy SMP algorithm. The chess engine implemented in the thesis ended up with an estimated ELO rating of 2238. The lazy SMP algorithm was successfully implemented, doubling the engines search speed using 4 threads on a multicore processor. Another aim of this thesis was to act as a starting compendium for aspiring chess programmers. In chapter 2 Components of a Chess Engine many of the techniques and algorithms used in modern chess engines are discussed and presented in a digestible way, in a try to make the topics understandable. The information there is presented in chronological order in relation to how a chess engine can be programmed. i ii Contents 1 Introduction 1 1.1 The History of Chess Computers . .2 1.1.1 The Beginning of Chess Playing Machines . .2 1.1.2 The Age of Computers . .3 1.1.3 The First Chess Computer . .5 1.1.4 The Interest in Chess Computers Grow . .6 1.1.5 Man versus Machine . .6 1.1.6 Shannon’s Type A versus Shannon’s Type B Chess Computers . -
Python-Chess Release 1.6.1
python-chess Release 1.6.1 unknown Sep 16, 2021 CONTENTS 1 Introduction 3 2 Installing 5 3 Documentation 7 4 Features 9 5 Selected projects 13 6 Acknowledgements 15 7 License 17 8 Contents 19 8.1 Core................................................... 19 8.2 PGN parsing and writing......................................... 36 8.3 Polyglot opening book reading...................................... 44 8.4 Gaviota endgame tablebase probing................................... 45 8.5 Syzygy endgame tablebase probing................................... 47 8.6 UCI/XBoard engine communication................................... 49 8.7 SVG rendering.............................................. 61 8.8 Variants.................................................. 63 8.9 Changelog for python-chess....................................... 65 9 Indices and tables 71 Index 73 i ii python-chess, Release 1.6.1 CONTENTS 1 python-chess, Release 1.6.1 2 CONTENTS CHAPTER ONE INTRODUCTION python-chess is a chess library for Python, with move generation, move validation, and support for common formats. This is the Scholar’s mate in python-chess: >>> import chess >>> board= chess.Board() >>> board.legal_moves <LegalMoveGenerator at ... (Nh3, Nf3, Nc3, Na3, h3, g3, f3, e3, d3, c3, ...)> >>> chess.Move.from_uci("a8a1") in board.legal_moves False >>> board.push_san("e4") Move.from_uci('e2e4') >>> board.push_san("e5") Move.from_uci('e7e5') >>> board.push_san("Qh5") Move.from_uci('d1h5') >>> board.push_san("Nc6") Move.from_uci('b8c6') >>> board.push_san("Bc4") Move.from_uci('f1c4') >>> board.push_san("Nf6") Move.from_uci('g8f6') >>> board.push_san("Qxf7") Move.from_uci('h5f7') >>> board.is_checkmate() True >>> board Board('r1bqkb1r/pppp1Qpp/2n2n2/4p3/2B1P3/8/PPPP1PPP/RNB1K1NR b KQkq - 0 4') 3 python-chess, Release 1.6.1 4 Chapter 1. Introduction CHAPTER TWO INSTALLING Download and install the latest release: pip install chess 5 python-chess, Release 1.6.1 6 Chapter 2. -
Estimating Total Search Space Size for Specific Piece Sets in Chess
Estimating Total Search Space Size for Specific Piece Sets in Chess Azlan Iqbal1 ABSTRACT Automatic chess problem or puzzle composition typically involves generating and testing various different positions, sometimes using particular piece sets. Once a position has been generated, it is then usually tested for positional legality based on the game rules. However, it is useful to be able to estimate what the search space size for particular piece combinations is to begin with. So if a desirable chess problem was successfully generated by examining ‘merely’ 100,000 or so positions in a theoretical search space of about 100 billion, this would imply the composing approach used was quite viable and perhaps even impressive. In this article, I explain a method of calculating the size of this search space using a combinatorics and permutations approach. While the mathematics itself may already be established, a precise method and justification of applying it with regard to the chessboard and chess pieces has not been documented, to the best of our knowledge. Additionally, the method could serve as a useful starting point for further estimations of search space size which filter out positions for legality and rotation, depending on how the automatic composer is allowed to place pieces on the board (because this affects its total search space size). 1 INTRODUCTION Automatic chess problem composition is a relatively unexplored area of artificial intelligence compared to actual chess-playing. The primary reason for this is likely that playing chess can be done quite well using a combination of well-designed heuristics and relatively high computational processing speed and memory. -
Playing the Perfect Kriegspiel Endgame
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Theoretical Computer Science 411 (2010) 3563–3577 Contents lists available at ScienceDirect Theoretical Computer Science journal homepage: www.elsevier.com/locate/tcs Playing the perfect Kriegspiel endgame Paolo Ciancarini ∗, Gian Piero Favini Dipartimento di Scienze dell'Informazione, University of Bologna, Italy article info a b s t r a c t Article history: Retrograde analysis is an algorithmic technique for reconstructing a game tree starting Received 16 August 2009 from its leaves; it is useful to solve some specific subsets of a complex game, for example Received in revised form 9 May 2010 a Chess endgame, achieving optimal play in these situations. Position values can then be Accepted 19 May 2010 stored in ``tablebases'' for instant access, in order to save analysis time, as is the norm Communicated by H.J. Van den Herik in professional chess programs. This paper shows that a similar approach can be used to solve subsets of certain imperfect information games such as Kriegspiel (invisible Chess) Keywords: endgames. Using a brute force retrograde analysis algorithm, a suitable data representation Game theory Kriegspiel and a special lookup algorithm, one can achieve perfect play, with perfection meaning Retrograde analysis fastest checkmate in the worst case and without making any assumptions on the opponent. Chess We investigate some Kriegspiel endgames (KRK, KQK, KBBK and KBNK), building the corresponding tablebases and casting light on some long standing open problems. ' 2010 Elsevier B.V. All rights reserved. 1. Introduction In a zero-sum game of perfect information, Zermelo's theorem [1] ensures that there is a perfect strategy allowing either player to obtain a guaranteed minimum reward. -
101 Tactical Tips
0 | P a g e 101 Tactical Tips By Tim Brennan http://tacticstime.com Version 1.00 March, 2012 This material contains elements protected under International and Federal Copyright laws and treaties. Any unauthorized reprint or use of this material is prohibited 101 Tactical Tips Table of Contents Introduction ............................................................................................................................................................ 1 101 Tactical Tips Openings and Tactics ............................................................................................................. 2 Books and Tactics .................................................................................................................. 4 Computers and Tactics .......................................................................................................... 6 Quotes about Tactics ............................................................................................................. 9 Tactics Improvement ............................................................................................................ 12 Tactics and Psychology ........................................................................................................ 14 Tactics Problems .................................................................................................................. 16 Tactical Motifs ..................................................................................................................... 17 Tactics