Table of Contents

1 The General Statement.- Definition of an Inexact Task.- Inexact Tasks and Control Systems.- Two Methods for Solving Inexact Problems.- The Goal of the Game and the Scoring Function.- Goal and Prognosis (The Optimal Variation).- Multi-level Control Systems.- Types of Multi-level Systems.- Advantages of the General Goal.- The Method for Connecting the Optimal Variations of the Components for Types C and E Regimes.- Computer Programs and Humans.- The Expansion of Artifical Intelligence.- 2 Methods for Limiting the Search Tree.- Truncation.- The Goal of an Inexact Game.- The Scoring Function.- Breaking Off a Variation.- The Pruning of Branches.- The Horizon.- Two Trees: The Mathematical Model (MM).- The Stratification of the System.- Three General Limitation Principles.- Improving the Results of a Search.- 3 The Search for a Solution and Historical Experience.- The Search for a Solution by Association.- The Handbook Method of Searching.- 4 An Example of the Solution of an Inexact Problem (Chess).- A. The Search for a Move in an Original Situation.- The Truncated Search Tree.- The Goal of the Inexact Game in Chess.- The Scoring Function: Two Components.- Breaking Off a Variation and Suspension of Play.- The Horizon.- Chess as a Three-Level System.- The First Level-A Piece with a Trajectory.- The Second Level-A Field of Play.- The Third Level-The Ensemble of All Fields (MM).- The Search Tree and the Minimax Procedure.- The Technique for Defining Trajectories.- The Technique for Forming Fields.- The Positional Component of the Scoring Function.- Priorities for Including in the Search Those Pieces and Fields that Take Part in the Play.- The Inclusion of a Field in the Play.- The Repetition of Moves at a Node.- The Depth of a Search and the Inclusion of Fields in It.- The Pruning of Branches.- Three States of a Field (The Active Mathematical Model).- Keeping the MM in Mind at a Terminal Node.- A Technical Question.- B. The Use of Historical Experience.- The Library of Openings.- The Library of Middle Games.- The Endgame Library.- 5 Three Endgame Studies (An Experiment).- 6 The Second World Championship.- KAISSA-CHESS 4.6.- Conclusions.- Appendix 1.- Fields of Play (by B. M. Stilman).- 1. The Formation of Fields and the Search Within Them.- 1.1. The Concept of a Field.- 1.2. The Search Procedure in the Initial Position.- 1.3. The Formation of Fields During the Search-An Example.- 1.4. Formation of a Field.- 1.5. Storage of Information about Sheaves of Trajectories in Computer Memory. Linked Lists.- 1.6. Information on the Trajectories of a Field.- 1.8. Computing the Length of a Denial Trajectory.- 1.9. Correction of the Sighting Method.- 1.10. The Pseudosearch.- 1.11. The Extent of the Climb Up a Branch in the Pseudosearch.- 1.14. Freezing a Trajectory for Lack of a Connection to an Active One.- 1.15. Criteria for Freezing.- 1.16. The Algorithm for Freezing.- 1.18. Trajectory and Field.- 2. The Choice of Moves in an Ensemble of Fields (The Mathematical Model).- 2.1. The Goal of the Game and the Ending of a Variation.- 2.2. The Criteria for Breaking Off a Variation in the Search.- 2.3. Testing the Criteria for Ending a Variation.- 2.4. Pruning Branches by the Minimax Principle. On the Branch-and-Bound Method.- 2.5. Pruning Branches by the Worst Case Method.- 2.6. Priority of Moves in a Search.- 2.7. Analysis of the Trajectories of a Sheaf for Inclusion in the Search.- 2.8. Analysis of Trajectories for Forking.- 2.9. Retreat and Deblockade.- 2.10. Pruning in the Presence of Branching in a Sheaf of Trajectories.- 2.11. The Structure of the Search Tree.- 2.12. A New Content of Known Procedures.- Appendix 2 The Positional Estimate and Assignment of Priorities (by M. A. Tsfasman and B. M. Stilman).- Appendix 3 The Endgame Library in PIONEER (Using Historical Experience by the Handbook Method and the Outreach Method) (by A. D. YUDIN).- 3.1. Introduction.- 3.2. Formulation of the Problem.- 3.3. Configurations.- 3.4. The Boundary Effect. Decomposition Formulae.- 3.5. Symmetries.- 3.6. The Structure of the Library. Classes. Coding of the Information.- 3.7. Organization of the Information in the Form of Two-Dimensional Tables with Subordination of Entries.- 3.8. The Algorithm for Using the Endgame Library (The Search for Exact Coincidence).- 3.9. Examples of the Operation of the Subroutine for Using the Endgame Library.- 3.10. Outreach for a Library Position.- 3.11. The Search for Nearby Positions.- 3.12. Filter with Respect to the Pawn Structure.- 3.13. The "One Color-Different Color" Filter.- 3.14. Filters Within a Set of Positions.- 3.15. Finding a Group of Neighboring Positions.- 3.16. Implementation of the Outreach Method. Anti-outreach.- 3.17. Entry from the Move-Search Routine.- 3.18. Outreach and Exact Coincidence.- 3.19. The Potential for Wide Use of Library Rules in PIONEER.- 3.20. The Breakoff Criterion Based on the Rule of the Square.- 3.21. Conclusion.- Appendix An Associative Library of Fragments (by A. I. Reznitsky and A. D. Yudin).- References.- Glossary of Terms.- Index of Notation.