Ph.D. dissertation "Bi-directional and heuristic search in path problems" (Stanford, Computer Science, 1970) summarized in this article in Machine Intelligence 6 (1971).In the uni-directional algorithms, the search proceeds from an initial nodeforward until the goal node is encountered. Problems for which the goal nodeis explicitly known can be searched backward from the goal node. Analgorithm combining both search directions is bi-directional.This method has not seen much use because book-keeping problems werethought to outweigh the possible search reduction. The use of hashingfunctions to partition the search space provides a solution to some of theseimplementation problems. However, a more serious difficulty is involved.To realize significant savings in bi-directional search, the forward andbackward search trees must meet in the 'middle' of the space. The potentialbenefits from this technique motivates this paper's examination of thetheoretical and practical problems in using bi-directional search.

In Meltzer, Bernard and Donald Michie (Eds.), Machine Intelligence 5. Edinburgh University Press.

Note: PDF of full volume downloadable by clicking on title above (32.8 MB). Selected individual chapters available from the links below.CONTENTSINTRODUCTORY MATERIALMATHEMATICAL FOUNDATIONS1 Program scheme equivalences and second-order logic. D. C. COOPER 32 Programs and their proofs: an algebraic approach.R. M. BURSTALL and P. J. LANDIN 173 Towards the unique decomposition of graphs. C. R. SNOW andH. I. SCOINS 45THEOREM PROVING4 Advances and problems in mechanical proof procedures. D. PRAWITZ 595 Theorem-provers combining model elimination and Tesolution.D. W. LOVELAND 736 Semantic trees in automatic theorem-proving. R. KOWALSKI andP. J. HAYES 877 A machine-oriented logic incorporating the equality relation.E. E. SIBERT 1038 Paramodulation and theorem-proving in first-order theories withequality. G. ROBINSON and L. Wos 1359 Mechanizing higher-order logic. J. A. ROBINSON 151DEDUCTIVE INFORMATION RETRIEVAL10 Theorem proving and information retrieval. J. L. DARLINGTON 17311 Theorem-proving by resolution as a basis for question-answeringsystems. C. CORDELL GREEN 183MACHINE LEARNING AND HEURISTIC PROGRAMMING12 Heuristic dendral: a program for generating explanatory hypothesesin organic chemistry. B. BUCHANAN, G. SUTHERLAND andE. A. FEIGENBAUM 20913 A chess-playing program. J. J. SCOTT 25514 Analysis of the machine chess game. I. J. GOOD 26715 PROSE—Parsing Recogniser Outputting Sentences in English.D. B. VIGOR, D. URQUHART and A. WILKINSON 27116 The organization of interaction in collectives of automata. 285V. I. VARSHAVSKY COGNITIVE PROCESSES: METHODS AND MODELS17 Steps towards a model of word selection. G. R. Kiss 31518 The game of hare and hounds and the statistical study of literaryvocabulary. S. H. STOREY and M. A. MAYBREY 33719 The holophone —recent developments. D. J. WILLSHAW andH. C. LONGUET-HIGGINS 349PATTERN RECOGNITION20 Pictorial relationships — a syntactic approach. M. B. CLOWES 36121 On the construction of an efficient feature space for optical characterrecognition. A. W. M. COOMBS 38522 Linear skeletons from square cupboards. C. J. HILDITCH 403PROBLEM-ORIENTED LANGUAGES23 Absys 1: an incremental compiler for assertions; an introduction.J. M. FOSTER and E. W. ELCOCK 423PRINCIPLES FOR DESIGNING INTELLIGENT ROBOTS24 Planning and generalisation in an automaton/environment system.J. E. DORAN 43325 Freddy in toyland. R. J. POPPLESTONE 45526 Some philosophical problems from the standpoint of artificialintelligence. J. MCCARTHY and P. J. HAYES 463INDEX 505 Machine Intelligence Workshop

This paper describes some recent experiments with a computer program which is capable of useful, or at least interesting, application to a number of different problems. The program, the Graph Traverser, has been described in detail in a previous paper (Doran & Michie 1966). However, we shall here need to view the basic algorithm from a rather more general standpoint, corresponding to an actual extension in the flexibility of the program, so that a restatement of what the program can do is desirable. The Graph Traverser, which is written in Elliott 4100 Algol, is potentially applicable to problem situations which can be idealised in the following way (see for comparison Newell and Ernst 1965). There is given a set of'states', which are connected by a set of'transformations', or, as I shall call them, 'operators'. An operator will be applicable to some, but not necessarily all, of the states and two distinct operators applied to either the same or distinct states may each give the same state as end -product. Most of the concepts to be used here which are related to the use of operators were discussed in a paper by Michie (1967). This type of problem situation is represented in Figure 1 by a graph (in the mathematical sense) to which have been added various labels.

Note: PDF of full volume downloadable by clicking on title above (26 MB). Selected individual chapters available from the links below. CONTENTSINTRODUCTION MATHEMATICAL FOUNDATIONS1 The morphology of prex—an essay in meta-algorithmics. J. LAS KS 32 Program schemata. M. S. PATE RSON 193 Language definition and compiler validation. J. J. FLORENTIN 334 Placing trees in lexicographic order. H. I.S COINS 43 THEOREM PROVING5 A new look at mathematics and its mechanization. B. M ELTZER 636 Some notes on resolution strategies. B. MELTZER 717 The generalized resolution principle. J. A. ROBINSON 778 Some tree-paring strategies for theorem proving. D.LUCKHAM 959 Automatic theorem proving with equality substitutions andmathematical induction. J. L. D ARLINGTON 113 MACHINE LEARNING AND HEURISTIC PROGRAMMING10 On representations of problems of reasoning about actions.S.AMAREL 13111 Descriptions. E.W.ELCOCK 17312 Kalah on Atlas. A.G.BELL 18113 Experiments with a pleasure-seeking automaton: J. E. DORAN 19514 Collective behaviour and control problems. V.I.VARSHAVSKY 217 MAN—MACHINE INTERACTION15 A comparison of heuristic, interactive, and unaided methods ofsolving a shortest-route problem. D.MICHIE, J. G. FLEMING andJ. V.OLDFIELD 24516 Interactive programming at Carnegie Tech. A.H.BOND 25717 Maintenance of large computer systems—the engineer's assistant.M.H.J.BAYLIS 269 COGNITIVE PROCESSES: METHODS AND MODELS18 The syntactic analysis of English by machine. J.P.THORNE,P.BRATLEY and H.DEWAR 28119 The adaptive memorization of sequences. H.C.LONOUETHIGGINSand A.ORTONY 311 PATTERN RECOGNITION20 An application of Graph Theory in pattern recognition.C.J.HILDITCH 325 PROBLEM-ORIENTED LANGUAGES21 Some semantics for data structures. D. PARK 35122 Writing search algorithms in functional form. R.M.BURSTALL 37323 Assertions: programs written without specifying unnecessaryorder. J.M.FOSTER 38724 The design philosophy of Pop-2. R.J.POPPLESTONE 393 INDEX 403 Machine Intelligence Workshop

A new signature table technique is described together with an improved book learning procedure which is thought to be much superior to the linear polynomial method described earlier. Full use is made of the so called “alpha-beta” pruning and several forms of forward pruning to restrict the spread of the move tree and to permit the program to look ahead to a much greater depth than it other- wise could do. While still unable to outplay checker masters, the program’s playing ability has been greatly improved.See also:IEEE XploreAnnual Review in Automatic Programming, Volume 6, Part 1, 1969, Pages 1–36Some Studies in Machine Learning Using the Game of CheckersIBM J of Research and Development ll, No.6, 1967,601

Operations Research 14:699-719

E.A. Feigenbaum and J. Feldman (Eds.). Computers and Thought. McGraw-Hill, 1963. This collection includes twenty classic papers by such pioneers as A. M. Turing and Marvin Minsky who were behind the pivotal advances in artificially simulating human thought processes with computers. All Parts are available as downloadable pdf files; most individual chapters are also available separately. COMPUTING MACHINERY AND INTELLIGENCE. A. M. Turing. CHESS-PLAYING PROGRAMS AND THE PROBLEM OF COMPLEXITY. Allen Newell, J.C. Shaw and H.A. Simon. SOME STUDIES IN MACHINE LEARNING USING THE GAME OF CHECKERS. A. L. Samuel. EMPIRICAL EXPLORATIONS WITH THE LOGIC THEORY MACHINE: A CASE STUDY IN HEURISTICS. Allen Newell J.C. Shaw and H.A. Simon. REALIZATION OF A GEOMETRY-THEOREM PROVING MACHINE. H. Gelernter. EMPIRICAL EXPLORATIONS OF THE GEOMETRY-THEOREM PROVING MACHINE. H. Gelernter, J.R. Hansen, and D. W. Loveland. SUMMARY OF A HEURISTIC LINE BALANCING PROCEDURE. Fred M. Tonge. A HEURISTIC PROGRAM THAT SOLVES SYMBOLIC INTEGRATION PROBLEMS IN FRESHMAN CALCULUS. James R. Slagle. BASEBALL: AN AUTOMATIC QUESTION ANSWERER. Green, Bert F. Jr., Alice K. Wolf, Carol Chomsky, and Kenneth Laughery. INFERENTIAL MEMORY AS THE BASIS OF MACHINES WHICH UNDERSTAND NATURAL LANGUAGE. Robert K. Lindsay. PATTERN RECOGNITION BY MACHINE. Oliver G. Selfridge and Ulric Neisser. A PATTERN-RECOGNITION PROGRAM THAT GENERATES, EVALUATES, AND ADJUSTS ITS OWN OPERATORS. Leonard Uhr and Charles Vossler. GPS, A PROGRAM THAT SIMULATES HUMAN THOUGHT. Allen Newell and H.A. Simon. THE SIMULATION OF VERBAL LEARNING BEHAVIOR. Edward A. Feigenbaum. PROGRAMMING A MODEL OF HUMAN CONCEPT FORMULATION. Earl B. Hunt and Carl I. Hovland. SIMULATION OF BEHAVIOR IN THE BINARY CHOICE EXPERIMENT Julian Feldman. A MODEL OF THE TRUST INVESTMENT PROCESS. Geoffrey P. E. Clarkson. A COMPUTER MODEL OF ELEMENTARY SOCIAL BEHAVIOR. John T. Gullahorn and Jeanne E. Gullahorn. TOWARD INTELLIGENT MACHINES. Paul Armer. STEPS TOWARD ARTIFICIAL INTELLIGENCE. Marvin Minsky. A SELECTED DESCRIPTOR-INDEXED BIBLIOGRAPHY TO THE LITERATURE ON ARTIFICIAL INTELLIGENCE. Marvin Minsky.

... The literature does not include any general discussion of the outstanding problems of this field. In this article, an attempt will be made to separate out, analyze, and find the relations between some of these problems. Analysis will be supported with enough examples from the literature to serve the introductory function of a review article, but there remains much relevant work not described here.Proc. Institute of Radio Engineers 49, p. 8-30

In Proceedings of the Symposium on Mechanisation of Thought Processes, National Physical Laboratory, Teddington, England, London: H. M. Stationary Office, pp. 3-36