The radius of Sheffer functions over E(3).

Title: The radius of Sheffer functions over E(3).
Identifier: AAI9521248
identifier: 9521248
Creator: Beckman, Jeffrey.
Contributor: Adviser: T. C. Wesselkamper
Date: 1995
Language: English
Publisher: City University of New York.
Subject: Computer Science
Abstract: Through the operation of composition, a two-place Sheffer function over a set E(k) = {dollar}\{lcub}0,1,2\...,{lcub}\rm k{rcub}-1\{rcub}{dollar} is a function capable of generating all other two-place functions ranging over the same set. This dissertation introduces the radius of the Sheffer function as a measure of the efficiency with which it performs this task. The radius r is defined as the least natural number such that all functions may be formed with r or fewer compositions of the Sheffer function.;The case of two-place functions over E(3) is examined in detail. It is demonstrated that the 3,774 Sheffer functions may be partitioned into 322 mutually exclusive classes, each having a single value of the radius. Measurements of the radius are presented for all 322 classes, with values ranging from 7 to 25.;A set of 5 conditions on the operation table of a Sheffer function is presented that serves to distinguish the efficient functions from the inefficient ones.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.