Showing papers in "Journal of the ACM in 1969"

New Methods in Automatic Extracting

Abstract: This paper describes new methods of automatically extracting documents for screening purposes, i.e. the computer selection of sentences having the greatest potential for conveying to the reader the substance of the document. While previous work has focused on one component of sentence significance, namely, the presence of high-frequency content words (key words), the methods described here also treat three additional components: pragmatic words (cue words); title and heading words; and structural indicators (sentence location).The research has resulted in an operating system and a research methodology. The extracting system is parameterized to control and vary the influence of the above four components. The research methodology includes procedures for the compilation of the required dictionaries, the setting of the control parameters, and the comparative evaluation of the automatic extracts with manually produced extracts. The results indicate that the three newly proposed components dominate the frequency component in the production of better extracts.

On the Length of Programs for Computing Finite Binary Sequences: statistical considerations

Abstract: An attempt is made to carry out a program (outlined in a previous paper) for defining the concept of a random or patternless, finite binary sequence, and for subsequently defining a random or patternless, infinite binary sequence to be a sequence whose initial segments are all random or patternless finite binary sequences. A definition based on the bounded-transfer Turing machine is given detailed study, but insufficient understanding of this computing machine precludes a complete treatment. A computing machine is introduced which avoids these difficulties.

Continuous Skeletons from Digitized Images

Abstract: An algorithm for the determination of the skeleton of a polygonal figure is presented. The propagation of the figure contour is simulated analytically. All skeleton branch points are obtained, in an order which depends on their distance from the contour, together with the equations of the skeleton branches connecting them. The computing time for polygons with few concave vertices is roughly proportional to the number of sides.

Toeplitz Matrix Inversion: The Algorithm of W. F. Trench

Abstract: The algorithm of W F Trench for the inversion of Toeplitz matrices is presented with a detailed proof for the case of non-Hermitian matrices The only condition necessary to insure the validity of the algorithm is that all principal minors be nonzero

A Simplified Format for the Model Elimination Theorem-Proving Procedure

Abstract: An alternate approach to the formulation of the Model Elimination proof pro­cedure is presented. By exploiting fully the ability to linearize the procedure format (isolating the format from a tree structure form) and by representing lemmas by clauses, the description of the Model Elimination procedure is greatly simplified.

Experiments With Some Programs That Search Game Trees

Abstract: Many problems in artificial intelligence involve the searching of large trees of alternative possibilities—for example, game-playing and theorem-proving. The problem of efficiently searching large trees is discussed. A new method called “dynamic ordering” is described, and the older minimax and Alpha-Beta procedures are described for comparison purposes. Performance figures are given for six variations of the game of kalah. A quantity called “depth ratio” is derived which is a measure of the efficiency of a search procedure. A theoretical limit of efficiency is calculated and it is shown experimentally that the dynamic ordering procedure approaches that limit.

An Infinite Hierarchy of Context-Free Languages

Abstract: By generalizing the notions of a one counter machine and of a finite turn pushdown store automaton, it is possible to define an omega 2-hierarchy of families of context-free languages such that each subfamily is infinite, closed under union, concatenation and closure, homomorphism, intersection with regular sets and inverse homomorphism and reversal. Each subfamily can be characterized in a manner akin to the Chomsky-Schutzenberger characterization of the context-free languages. Whenever two subfamilies are incomparable it is undecidable whether a member of one belongs to the other.

On the Simplicity and Speed of Programs for Computing Infinite Sets of Natural Numbers

Abstract: It is suggested that there are infinite computable sets of natural numbers with the property that no infinite subset can be computed more simply or more quickly than the whole set. Attempts to establish this without restricting in any way the computer involved in the calculations are not

Some Results on Tape-Bounded Turing Machines

Abstract: Classes of tape-bounded Turing machines similar to the on-line and off-line Turing machines, but without the restrictions that each machine halt and be deterministic, are studied. It is shown that the lower bounds on tape complexity of [1] depend on neither the halting assumption nor determinism. The existence of a dense hierarchy of complexity classes likewise does not depend on the halting assumption, and it is shown that below log n tape complexity there exists a dense hierarchy of complexity classes for two-way nondeterministic devices. It is also shown that the complexity classes of one-way, nondeterministic machines below linear large complexity are not closed under complementation and are larger that the corresponding deterministic complexity class.

Linear Multistep Methods for Volterra Integro-Differential Equations

Abstract: The Dahlquist stability analysis for ordinary differential equations is extended to the case of Volterra integro-differential equations. Thus the standard multistep methods can be generalized to furnish algorithms for solving integro-differential equations. Special starting procedures are discussed, and some numerical examples are presented.

The Recursive Unsolvability of the Decision Problem for the Class of Definite Formulas

Abstract: A class of formulas of the first-order predicate calculus, the definite formulas has recently been proposed as the formal representation of the “reasonable” questions to put to a computer in the context of an actual data retrieval system, the Relational Data File of Levien and Maron. It is shown here that the decision problem for the class of definite formulas is recursively unsolvable. Hence there is no algorithm to decide whether a given formula is definite.

Properties of Programs and the First-Order Predicate Calculus

Abstract: This paper is concerned with the relationship of the termination problem for programs and abstract programs to the validity of certain formulas in the first-order predicate calculus. By exploiting this relationship, subclasses of abstract programs for which the termination problem is decidable can be isolated. Moreover, known proof procedures for the first-order predicate calculus (e.g. resolution) can be applied to prove the termination of both programs and abstract programs. The correctness and equivalence problems of abstract programs are shown to be reducible to the termination problem.

An Algorithm for Finding a Minimum Equivalent Graph of a Digraph

Abstract: : A directed graph or digraph can be thought of as a communication network among a set of persons, where the vertices of the graph correspond to persons and edges of the graph to directed channels of communication from one person to another. A person is said to be able to 'reach' another if he can send a message to that person. The present paper gives an algorithm for finding the maximum number of edges that can be removed from a digraph without affecting its reachability properties. (Author)

Notes on the Adaptive Simpson Quadrature Routine

Abstract: A definif, ive account of the principles of automatic integration appears in the book Numerical Integration by Davis and Rabinowitz [2]. Several algorithms and routines are described which can be used to obtain an approximation having a prescribed tolerance e to a given definite integral. In general, the user provides only the limits of integration A and B, the desired tolerance e, and a subroutine FUN(X) which calculates the integrand. The automatic integration scheme, in the form of a subroutine, provides a result, thus \"relieving the user of any need to think.\" One of the earlier, and certainly one of the most successful, routines of this type is the adaptive Simpson routine, published in algorithm form in 1962 (McKeeman [6]). Modifications of this routine (McKeeman [7], [9] and McKeeman and Tesler [8]) have been widely used in computing centers ever since. However, to the author's knowledge there is no account of this routine or error analysis of it in the open literature. In this paper the method on which the routine is based is investigated with a view to making improvements. It is perhaps pertinent to mention the form improvements in an automatic integration routine might take. In general, the required tolerance or accuracy e is given and a \"good\" routine attempts to attain only this accuracy using as few function evaluations as possible. In practice, the routine produces a result of greater accuracy. I t is a defect if greater accuracy is obtained at a cost of additional function evaluations, even if the increase in accuracy is considerable and the number of additional function evaluations is marginal. In fact one modification mentioned above was introduced by MeKeeman in all at tempt to correct to some extent a defect of this type. Bearing this in mind, improvements result if any changes of the following nature can be made: (i) a change which produces a result of lower accuracy, but still within the prescribed accuracy e, with a consequent reduction in the number of function evaluations required;

Semi-Automated Mathematics

Abstract: The fifth in a series of experiments in semi-automated mathematics is described These experiments culminated in large complex computer programs which allow a mathematician to prove mathematical theorems on an man/machine basis SAM V, the fifth program, is oriented primarily toward the development of efficient automatic techniques for handling some of the more basic processes of mathematical deduction, and toward the realization of efficient real-time interaction between man and machine through the use of cathode-ray tube displays SAM V's most notable success is the solution of an open problem in lattice theory

One Man's View of Computer Science

Abstract: A number of observations and comments are directed toward suggesting that more than the usual engineering flavor be given to computer science. The engineering aspect is important because most present difficulties in this field do not involve the theoretical question of whether certain things can be done, but rather the practical question of how can they be accomplished well and simply.The teaching of computer science could be made more effective by various alterations, for example, the inclusion of a laboratory course in programming, the requirement for a strong minor in something other than mathematics, and more practical coding and less abstract theory, as well as more seriousness and less game playing.

Analysis and Optimization of Disk Storage Devices for Time-Sharing Systems

Abstract: A major limitation for time-sharing systems is the time delay encountered in transferring records between central “fast” memory and peripheral memory devices. In this paper the transfer characteristics of disk storage devices are considered. Expected seek time and expected rotational latency are taken as measures of performance for the disk. The following aspects of disk files and their behavior are considered: the speed profile of the positioning mechanism and its effect on seek time; effects of the probability distribution of information stored on tracks; track overflow of records; dynamic queuing strategies; reduction of rotation time by buffered read techniques; and strategies for using multiple-arm devices.

A Cycle Generation Algorithm for Finite Undirected Linear Graphs

Abstract: When the algorithms of J. T. Welch, Jr. were implemented it was discovered that they did not perform as described. The generation of all cycles from a basis is faulty. The generation of the basis is apparently correct. A modified version of Welch's Algorithm 3 is presented. The reasons for modifying Welch's algorithms are presented with examples.

A Note on Star-Free Events

Abstract: It is shown that a short proof of the equivalence of star-free and group-free regular events is possible if one is willing to appeal to the Krohn-Rhodes machine decomposition theorem.

Organization of Large Scale Fourier Processors

Abstract: AnSTRACT. The organization of a special purpose processor for computing the Fourier transform of a data set of N = 2 ~ complex numbers is considered. A limited amount of parallel computation facility is assumed, and organizations are sought that make efficient use of the available parallel capacity and can use memories of limited speed and therefore of relatively low cost. The proposed organization not only accomplishes this but also can be programmed, without loss of speed, to deliver the computed spectra in proper order. In addition, it is adapted to the handling of very large data bases on a continuous production basis, where the rate of flow of data is too great for serial processing.

Erratum: `` Analysis of a Drum Input/Output Queue Under Scheduled Operation in a Paged Computer System''

Abstract: Properly scheduling the usage of input output devices is an important aspect of the design of modern multiprogramming systems featuring a paged environment. In this paper magnetic drums in the role of auxiliary memories are studied in the context of these systems. It is the nature of the drum, its usage by the system, and the organization of information on the drum are discussed in the light of current system designs. Mathematical models are then defined such that two extremes in scheduling disciplines are represented in a system in which page requests are assumed to arrive singly and at random. The analysis leads to results for a measure of drum utilization, a generating function for the queue length probabilities in equilibrium, the mean queue length, and the mean waiting time. Finally, the significance of the results is discussed along with some examples.

Toward a Theory of Enumerations

Abstract: An attempt is made to show that there is much work in pure recursion theory which implicitly treats computational complexity of algorithmic devices which enumerate sets. The emphasis is on obtaining results which are independent of the particular model one uses for the enumeration technique and which can be obtained easily from known results and known proofs in pure recursion theory.First, it is shown that it is usually impossible to define operators on sets by examining the structure of the enumerating devices unless the same operator can be defined merely by examining the behavior of the devices. However, an example is given of an operator which can be defined by examining the structure but which cannot be obtained merely by examining the behavior.Next, an example is given of a set which cannot be enumerated quickly because there is no way of quickly obtaining large parts of it (perhaps with extraneous elements). By way of contrast, sets are constructed whose elements can be obtained rapidly in conjunction with the enumeration of a second set, but which themselves cannot be enumerated rapidly because there is no easy way to eliminate the members of the second set.Finally, it is shown how some of the elementary parts of the Hartmanis-Stearns theory can be obtained in a general setting.

Sufficient Conditions for the Success of GPS

Abstract: A formal model of a problem is developed and its relationship to the General Problem Solver (GPS) is discussed. Before GPS can work on a problem it must be given differences, a difference-ordering, and a table of connections, in addition to the specifications of a problem. Formal definitions of this additional information are given, and sufficient conditions for the success of GPS are derived. These conditions point out the utility of differences and a difference-ordering that yield a “triangular” table of connections. Several different formulations of the Tower of Hanoi are given to illustrate the formal concepts. The use of subproblems in narrowing search is discussed.

A Syntax-Analysis Procedure for Unambiguous Context-Free Grammars

Abstract: A syntax-analys is Mgorithm is presented for a language generated by an unambiguous context-free grammar in a number of e lementary operat ions proportional to n = log n, where n is the length of a given string, using a random access memory. The amount of memory required for the a lgor i thm is proport ional to n 2 log n. The proposed algori thm is a modified version of Cocke's a lgor i thm and utilizes a eertair, proper ty of unambiguous normal grammars .

Automorphisms of Polyadic Automata

Abstract: This paper is a continuation of the studies of Fleck, Weeg, and others concerning the theory of automorphisms of ordinary automata and of the work of Gil pertaining to time varying automata. A certain restricted class of time-varying automata, namely the class of polyadic automata, is investigated in detail. The results of an investigation of relationships concerning the group of automorphisms, the polyadic group of defined polyadic automata and the structure of the polyadic automation and the ordinary automata associated and with the polyadic automaton is presented.

A Time-Sharing Queue with a Finite Number of Customers

Abstract: A time-sharing queue serving a finite number of customers is described. It is assumed that both the service time and the time elapsing between termination of service and the next arrival of the same customer at the queue (service station) are exponential. The model was studied by Krishnamoorthi and Wood, but their results are not in complete agreement with the results of this paper. In addition, some new results are presented in terms of steady-state expectations.

File Organization: On the Selection of Random Access Index Points for Sequential Files

Abstract: The construction of a hierarchy of indexes (the indexed sequential access method) is one means of providing rapid random access to sequential files. An examination is made of the consequences of partially or completely replacing one or more index levels by linear interpolation procedures. For all possible configurations of the several types of key distributions investigated, linear interpolation on the average provides significant performance improvements. Typically, the two accesses required to obtain track index and data are reduced to 1.1 to 1.7 accesses per record. Extremely unusual key distribution will, however, raise the number of accesses required above 2.