**On Ianov's Program Schemata**

J. D. Rutledge

Pages: 1-9

DOI: 10.1145/321203.321204

Ianov has defined a formal abstraction of the notion of program which represents the sequential and control properties of a program but suppresses the details of the operations. For these schemata he defines a notion corresponding to computation...

**Tape Sets and Automata**

R. R. Brown

Pages: 10-14

DOI: 10.1145/321203.321205

Tape sets and a tape set product are defined, and relationships are found between a table of products of tape sets and elements in the operation-preserving group of a finite automaton.

**Universality of Tag Systems with P = 2**

John Cocke, Marvin Minsky

Pages: 15-20

DOI: 10.1145/321203.321206

By a simple direct construction it is shown that computations done by Turing machines can be duplicated by a very simple symbol manipulation process. The process is described by a simple form of Post canonical system with some very strong...

**SNOBOL , A String Manipulation Language**

D. J. Farber, R. E. Griswold, I. P. Polonsky

Pages: 21-30

DOI: 10.1145/321203.321207

SNOBOL is a programming language for the manipulation of strings of symbols. A statement in the SNOBOL language consists of a rule that operates on symbolically named strings. The basic operations are string formation, pattern matching and...

**Mixed Congruential Random Number Generators for Binary Machines**

T. E. Hull, A. R. Dobell

Pages: 31-40

DOI: 10.1145/321203.321208

Random number generators of the mixed congruential type have recently been proposed. They appear to have some advantages over those of the multiplicative type, except that their statistical behavior is unsatisfactory in some cases. It is shown...

**Calculations with Pseudo-Random Numbers**

Frank Stockmal

Pages: 41-52

DOI: 10.1145/321203.321209

Two pseudo-random number generators are considered, the multiplicative congruential method and the mixed congruential method. Some properties of the generated sequences are derived, and several algorithms are developed for the evaluation of...

**Two New Classes of Algorithms for Finding the Eigenvalues and Eigenvectors of Real Symmetric Matrices**

C. Donald La Budde

Pages: 53-58

DOI: 10.1145/321203.321210

The algorithms described in this paper are essentially Jacobi-like iterative procedures employing Householder orthogonal similarity transformations and Jacobi orthogonal similarity transformations to reduce a real symmetrix matrix to diagonal...

**A Direct Method for Chebyshev Approximation by Rational Functions**

Josef Stoer

Pages: 59-69

DOI: 10.1145/321203.321211

**Tables of the Generalized Stirling Numbers of the First Kind**

William F. Pickard

Pages: 70-78

DOI: 10.1145/321203.321212

The generalized Stirling numbers of the first kind are defined, certain of their basic properties are discussed, and tables are given for the square grid k = 0(1)10 and j = 0(1)10 with l =...

**A Mathematical Method for the Automatic Scaling of a Function**

T. Giammo

Pages: 79-83

DOI: 10.1145/321203.321213

This paper describes a procedure for producing scales for use in automatic plotting of data. The scale and associated origin of the plot produced by this procedure are “round numbers.” The procedure itself is independent of the range...

**Application of Ternary Algebra to the Study of Static Hazards**

Michael Yoeli, Shlomo Rinon

Pages: 84-97

DOI: 10.1145/321203.321214

This paper is concerned with the study of static hazards in combinational switching circuits by means of a suitable ternary switching algebra. Techniques for hazard detection and elimination are developed which are analogous to the...

**Estimation of Power Spectral Density by Filters**

E. J. Gauss

Pages: 98-103

DOI: 10.1145/321203.321215

An algorithm is presented which differs from previous methods by being more adapted for searching over wide frequency ranges and which permits the estimation of spectral density as a function of time as well as of frequency. The algorithm may...

**Message Route Control in a Large Teletype Network**

Maurice Pollack

Pages: 104-116

DOI: 10.1145/321203.321216