**Probability Models for Multiprogramming Computer Systems**

D. P. Gaver, Jr.

Pages: 423-438

DOI: 10.1145/321406.321407

A probabilistic model is developed for a multiprogramming computer configuration, i.e., one in which several program segments are simultaneously in main memory (core). The model relates speed and number of input-output devices, core size, and...

**Production and Stabilization of Real-Time Task Schedules**

G. K. Manacher

Pages: 439-465

DOI: 10.1145/321406.321408

A model for multiprocessor control is considered in which jobs are broken into various pieces, called tasks. Tasks are executed by single processing units. In this paper the structure controlling the assignment of tasks to...

**Roots of Star Events**

J. A. Brzozowski

Pages: 466-477

DOI: 10.1145/321406.321409

A regular event W is a star event if there exists another event V such that W = V*. In that case, V is called a root of W....

**Some Bounds on the Storage Requirements of Sequential Machines and Turing Machines**

Richard M. Karp

Pages: 478-489

DOI: 10.1145/321406.321410

Any sequential machine M represents a function fM from input sequences to output symbols. A function f is representable if some finite-state sequential...

**Parenthesis Grammars**

Robert McNaughton

Pages: 490-500

DOI: 10.1145/321406.321411

A decision procedure is given which determines whether the languages defined by two parenthesis grammars are equal.

**Matrix Equations and Normal Forms for Context-Free Grammars**

Daniel J. Rosenkrantz

Pages: 501-507

DOI: 10.1145/321406.321412

The relationship between the set of productions of a context-free grammar and the corresponding set of defining equations is first pointed out. The closure operation on a matrix of strings is defined and this concept is used to formalize the...

**Analysis of Factorial Experiments Using Generalized Matrix Operations**

I. Oliver

Pages: 508-519

DOI: 10.1145/321406.321413

The computer analysis of factorial experiments is discussed in terms of a new generalized matrix notation which highlights the special properties of factorial designs. A method of calculating an analysis of a variance suitable for programming as...

**A Method for Constructing Circuit Codes**

Victor Klee

Pages: 520-528

DOI: 10.1145/321406.321414

A d-dimensional circuit code of spread s (also called SIBs, code or circuit code of minimum distance s) is a simple circuit Q in the graph...

**An Algorithm for Generating Stable Feedback Shift Registers of Order n**

Frederic J. Mowle

Pages: 529-542

DOI: 10.1145/321406.321415

It is shown in this paper that the stable feedback shift registers, when classified according to Hamming weight (the number of fundamental product terms in expanded sum of products form), are binomially distributed, i.e., are...

**On the Compatibility of a Given Solution With the Data of a Linear System**

J. L. Rigal, J. Gaches

Pages: 543-548

DOI: 10.1145/321406.321416

Some new theorems generalizing a result of Oettli and Prager are applied to the a posteriori analysis of the compatibility of a computed solution to the uncertain data of a linear system (or of a polynomial equation).

**Numerical Solution of Parabolic Partial Differential Equations With Two-Point Boundary Conditions by Use of the Method of Lines**

J. S. Hicks, J. Wei

Pages: 549-562

DOI: 10.1145/321406.321417

The Method of Lines, a numerical technique commonly used for solving partial differential equations on analog computers, is used to attain digital computer solutions of such equations. An extensive theoretical development is presented that...

**The Organization of Computations for Uniform Recurrence Equations**

Richard M. Karp, Raymond E. Miller, Shmuel Winograd

Pages: 563-590

DOI: 10.1145/321406.321418

A set equations in the quantities ai(p), where i = 1, 2, · · ·, m and p ranges over a set R of...

**Application of Parallel Processing to Numerical Weather Prediction**

A. B. Carroll, R. T. Wetherald

Pages: 591-614

DOI: 10.1145/321406.321419

The purpose of this study is to illustrate the application of a parallel network processing computing system to an important class of problems in hydrodynamics. The computing system selected for this study is a prototype of the SOLOMON parallel...