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#### Definability of Boolean Function Over Many-value Boolean Algebra

(Department of Computer Science, Virginia Polytechnic Institute & State University, 1974), CS74007-R

In this paper, the definability of functions over B_s is first briefly discussed. We then give necessary and sufficient conditions on the definable functions over B_2, boolean algebra of four values. An efficient algorithm ...

#### Storage Reduction Through Minimal Spanning Trees

(Department of Computer Science, Virginia Polytechnic Institute & State University, 1975), CS75003-R

In this paper, we shall show that a minimal spanning tree for a set of data can be used to reduce the amount of memory space required to store the data. Intuitively, the more points we have, the more likely our method ...

#### On the Minimal Total Path Length of a Spanning Tree

(Department of Computer Science, Virginia Polytechnic Institute & State University, 1974), CS74032-R

The notions of a balance node and the total path length with respect to a node u of a spanning tree are defined. We show that the total path length of a spanning tree with respect to u is minimal if and only if u is a ...

#### Computability Theory: An Introduction for Students of Computer Science

(Department of Computer Science, Virginia Polytechnic Institute & State University, 1975), CS75030-R

The primary goal of this book is to introduce the basic concepts of effective computability and to prepare the reader for the study of formal language theory, recursive function theory, and the theory of computational ...

#### Analysis of an Enumeration Algorithm for Unordered K-partitions of N

(Department of Computer Science, Virginia Polytechnic Institute & State University, 1974), CS74009-R

In many combinatorial problems, the need to compute the number of unrestricted partitions of n or to enumerate over the set of unrestricted partitions of n occurs frequently. Let two positive integers k and n be given, ...

#### An Extension of the Direct Method for Verifying Programs

(Department of Computer Science, Virginia Polytechnic Institute & State University, 1975), CS75022-R

A direct method based on a finite set of path formulas which describe the input-output relations of a given program can be used to verify programs containing no overlapping loops. One major difficulty in verifying programs ...