STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCEOverview
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STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
A Fast Algorithm for finding Dominators in a Flow Graph
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Book
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1 edition published in 1978 in English and held by 4 libraries worldwide This paper presents a fast algorithm for finding dominators in a flow graph. The algorithm uses depth-first search and an efficient method of computing functions defined on paths in trees. A simple implementation of the algorithm runs in O(m log n) time, where m is the number of edges and n is the number of vertices in the problem graph. A sophisticated implementation runs in O(M alpha (m, n)) time, where alpha(m, n) is a functional inverse of Ackermann's function. Both versions of the algorithm were implemented in Algol W, and tested on an IBM 370/168. The programs were compared with an implementation by Purdom and Moore of a straightforward O(mn) - time algorithm, and with a bit vector algorithm. The fast algorithm beat the straightforward algorithm and the bit vector algorithm on all but the smallest graphs tests.
PROJECT TECHNICAL REPORT
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Book
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3 editions published between 1968 and 1971 in English and held by 3 libraries worldwide Recent work of the Stanford Artificial Intelligence Project is summarized in several areas: Scientific hypothesis formation; Symbolic computation; Hand-eye systems; Computer recognition of speech; Board games; and Other projects. (Author).
The Fourteen Primitive Actions and Their Inferences
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Book
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1 edition published in 1973 in English and held by 3 libraries worldwide In order to represent the conceptual information underlying a natural language sentence, a conceptual structure was established that uses the basic actor-action-object framework. It was the intent that these structures have only one representation for one meaning, regardless of the semantic form of the sentence being r presented. Actions were reduced to their basic parts so as to effect this. It was found that only fourteen basic actions were needed as building blocks by which all verbs can be represented. Each of these actions has a set of actions or states which can be inferred when they are present. (Author).
Updating Formulae and a Pairwise Algorithm for Computing Sample Variances
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Book
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1 edition published in 1979 in English and held by 3 libraries worldwide A general formula is presented for computing the sample variance for a sample of size m + n given the means of variances for two subsamples of sizes m and n. This formula is used in the construction of a pairwise algorithm for computing the variance. Other applications are discussed as well, including the use of updating formulae in a parallel computing environment. We present numerical results and rounding error analyses for several numerical schemes. (Author).
Software Implementation of a New Method of Combinatorial Hashing
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Book
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1 edition published in 1975 in English and held by 3 libraries worldwide This is a study of the software implementation of a new method of searching with retrieval on secondary keys. A new family of partial match file designs is presented, the worst case is determined, a detailed algorithm and program are given and the average execution time is studied.
Some Linear Programming Aspects of Combinatorics
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Book
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1 edition published in 1975 in English and held by 3 libraries worldwide This is the text of a lecture given at the Conference on Algebraic Aspects of Combinatorics at the University of Toronto in January, 1975. The lecture was expository, aimed at an audience with no previous knowledge of linear programming.
The Macro Processing System STAGE2: Transfer of Comments to the Generated Text
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Book
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1 edition published in 1975 in English and held by 3 libraries worldwide This paper is a short description of a small extension of STAGE2, providing possibilities to copy comments etc. from the source text to the generated text. The description presupposes familiarity with the STAGE2 system: its purpose, use and descriptions, like (1) to (9). Only section 3 of this paper requires knowledge of the internal structures and working of the system, and that section is unnecessary for the plain use of the described feature. The extension, if not used, is completely invisible to the user: No rules, as described in the original literature, are changed. A user, unaware of the extension, will see no difference from the original version. (Author).
Computer Control of a Machine for Exploring Mars
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Book
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1 edition published in 1964 in English and held by 2 libraries worldwide Landing a 5000 pound package on Mars that would spend a year looking for life and making other measurements has been proposed. It is believed that this machine should be a stored program computer with sense and motor organs, and that the machine should be mobile. The author discusses the following points: Advantages of a computer controlled system; what the computer should be like; what we can feasibly program the machine to do given the present state of work on artificial intelligence; and, a plan for carrying out research in computer controlled experiments that will make the Mars machine as effective as possible. (Modified author abstract).
ALGORITHMS FOR MATRIX MULTIPLICATION
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Book
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1 edition published in 1970 in English and held by 2 libraries worldwide Strassen's and Winograd's algorithms for matrix multiplication are investigated and compared with the normal algorithm. Floating - point error bounds are obtained, and it is shown that scaling is essential for numerical accuracy using Winograd's method. In practical cases Winograd's method appears to be slightly faster than the other two methods, but the gain is, at most, about 20%. An attempt to generalize Strassen's method is described. (Author).
Empirical evidence for a proposed distribution of small prime gaps
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Book
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1 edition published in 1969 in English and held by 2 libraries worldwide The distribution of small gaps between adjacent prime numbers is studied. A model for this distribution is derived from probability arguments. Empirical evidence strongly supports this model. An asymptotic density function for twin primes is suggested, and support is given to the conjecture that there is an infinity of twin primes. (Author).
A computer system for writing and testing transformational grammars
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Book
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1 edition published in 1968 in English and held by 2 libraries worldwide For the past two years the Computational Linguistics Project in the Computer Science Department at Stanford University has been engaged in research leading to computer programs for accepting and manipulating transformational grammars corresponding to a version of the theory based on Chomsky's Aspects of the Theory of Syntax. These programs have been combined into a computer system for transformational grammar which accepts a transformational grammar in a natural format, and carries out the complete generation of sentences, from phrase structure generation, through lexical insertion and transformation. These programs are the first to handle complete sentence generation. The project has made some interesting contributions to linguistic theory, particularly in the areas of formal definition of grammars, lexical insertion, and traffic rules for transformations. The results obtained are described in reports which have been issued during the course of the project. To summarize these results the abstracts of the more important papers are included here. The bibliography attached to this report contains a list of current reports produced by the project. (Author).
Interval arithmetic determinant evaluation and its use in testing for a chebyshev system
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Book
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1 edition published in 1968 in English and held by 2 libraries worldwide Two recent papers by Hansen and by Hansen and R.R. Smith have shown how interval arithmetic (I.A.) can be used effectively to bound errors in matrix computations. This paper compares a method proposed by Hansen and R.R. Smith to straightforward use of I.A. in determinant evaluation. Computational results show what accuracy and running times can be expected when using I.A. for determinant evaluation. An application using I.A. determinants in a program to test a set of functions to see if they form a Chebyshev system is then presented. (Author).
RELAXATION METHODS FOR CONVEX PROBLEMS
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Book
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1 edition published in 1968 in English and held by 2 libraries worldwide Extensions and simplifications are made for convergence proofs of relaxation methods for nonlinear systems arising from the minimization of strictly convex functions. This work extends these methods to group relaxation, which includes an extrapolated form of Newton's method, for various orderings. A relatively simple proof is given for cyclic orderings, sometimes referred to as nonlinear overrelaxation, and for residual orderings where an error estimate is given. A less restrictive choice of relaxation parameter is obtained than that previously. Applications are indicated primarily to the solution of nonlinear elliptic boundary problems. (Author).
Floating-point number representations: base choice versus exponent range
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Book
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1 edition published in 1967 in English and held by 2 libraries worldwide A digital computer whose memory words are composed of r-state devices is considered. The choice of the base, beta, for the internal floating-point numbers on such a computer is discussed. Larger values of beta necessitate the use of more r-state devices for the mantissa, in order to preserve some 'minimum accuracy, ' leaving fewer r-state devices for the exponent of beta. As beta increases, the exponent range may increase for a short period, but it must ultimately decrease to zero. Of course, this behavior depends on what definition of accuracy is used. This behavior is analyzed for a recently proposed definition of accuracy which specifies when it is to be said that the set of q-digit base beta floating-point numbers is accurate to p-digits base t. The only case of practical importance today is t = 10 and r = 2; and in this case beta = 2 is always best. However, the analysis is done to cover all cases. (Author).
GRAEFFE'S METHOD FOR EIGENVALUES
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Book
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1 edition published in 1967 in English and held by 2 libraries worldwide Let an entire function F(z) of finite genus have infinitely many zeros which are all positive, and take real values for real z. Then it is shown how to give two-sided bounds for all the zeros of F in terms of the coefficients of the power series of F, and of coefficients obtained by Graeffe's algorithm applied to F.A simple numerical illustration is given for a Bessel function.
Determining the Chromatic Number of a Graph
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Book
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1 edition published in 1976 in English and held by 2 libraries worldwide Certain algorithms concerning coloring graphs involve the partial exploration of Zykov trees. We investigate the size of such trees, and prove that a certain class of branch-and-bound algorithms for determining the chromatic number of a graph requires in probability a number of steps which grows faster than exponentially with the number of vertices of the graph. (Author).
MINIMUM MULTIPLICATION FOURIER ANALYSIS
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Book
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1 edition published in 1965 in English and held by 2 libraries worldwide Fourier analysis and synthesis is a frequently used tool in applied mathematics but is found to be a time consuming process to apply on a digital computer and this fact may prevent the practical application of the technique. This paper describes an algorithm which uses the symmetries of the sine and cosine functions to reduce the number of arithmetic operations by a factor between 10 and 30. The algorithm is applicable to a finite fourier (or harmonic) analysis on 12 X 2 to the qth power values, where q is any integer> or = 0 and is applicable to a variety of end conditions. A complete and tested B5000 Algol program known as FOURIER12 is included. (Author).
Automatic Program Verification III: A Methodology for Verifying Programs
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Book
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1 edition published in 1974 in English and held by 2 libraries worldwide The paper investigates methods for applying an on-line interactive verification system designed to prove properties of PASCAL programs. The methodology is intended to provide techniques for developing a debugged and verified version starting from a program, that (a) is possibly unfinished in some respects, (b) may not satisfy the given specifications, e.g., may contain bugs, (c) may have incomplete documentation, (d) may be written in non-standard ways, e.g., may depend on user- defined data structures. The methodology involves (1) interactive application of a verification condition generator, an algebraic simplifier and a theorem-prover; (2) techniques for describing data structures, type constraints, and properties of programs and subprograms (i.e. lower level procedures); (3) the use of (abstract) data types in structuring programs and proofs.
Estimating the Efficiency of Backtrack Programs
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Book
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1 edition published in 1974 in English and held by 2 libraries worldwide One of the chief difficulties associated with the so-called backtracking technique for combinatorial problems has been the inability to predict the efficiency of a given algorithm, or to compare the efficiencies of different approaches, without actually writing and running the programs. This paper presents a simple method which produces reasonable estimates for most applications, requiring only a modest amount of hand calculation. The method should prove to be of considerable utility in connection with D.H. Lehmer's branch-and-bound approach to combinatorial optimization.
AUTOMATIC GRADING PROGRAMS
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1 edition published in 1965 in English and held by 2 libraries worldwide The ALGOL grader programs are presented for the computer evaluation of student ALGOL programs. One is for a beginner's program; it furnishes random data and checks answers. The other provides a searching test of the reliability and efficiency of a rootfinding procedure. There is a statement of the essential properties of a computer system, in order that grader programs can be effectively used. (Author). more
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