Exclusive-or Sum-of-products Expressions Research Articles

Exclusive or Sum of Complex Terms expressions minimization

This paper demonstrates both theoretically, through theorem proofs, and experimentally, that existing minimization algorithms for ESOP (Exclusive or Sum Of Products) expressions can be successfully used for minimizing ESCT (Exclusive or Sum of Complex Terms) expressions as well. ESCT expressions are more general than ESOP ones and being reversible are very useful for logic design and for quantum circuits. The field of ESOP minimization has received considerable attention along the years and a great number of research works can be found in the literature, in contrast to the ESCT minimization problem with much fewer works addressing it. The open problems of finding exact ESCT expressions for completely specified functions of more than six variables as well as the problem of finding exact ESCT expressions for incompletely specified functions are solved here based on ESOP principles, for the first time.

EXACT MINIMIZATION OF AND–EXOR EXPRESSIONS OF PRACTICAL BENCHMARK FUNCTIONS

We propose faster-computing methods for the minimization algorithm of AND–EXOR expressions, or exclusive-or sum-of-products expressions (ESOPs), and obtain the exact minimum ESOPs of benchmark functions. These methods improve the search procedure for ESOPs, which is the most time-consuming part of the original algorithm. For faster computation, the search space for ESOPs is reduced by checking the upper and lower bounds on the size of ESOPs. Experimental results to demonstrate the effectiveness of these methods are presented. The exact minimum ESOPs of many practical benchmark functions have been revealed by this improved algorithm.

AN APPLICATION OF ESOP EXPRESSIONS TO SECURE COMPUTATIONS

This paper gives an application of exclusive-or sum-of-products (ESOP) expressions to designing cryptographic protocols. That is, this paper deals with secure computations in a minimal model, and gives a protocol which securely computes every function by means of the techniques of ESOP expressions. The communication complexity of our protocol is proportional to the size of an obtained multiple-valued-input ESOP expression. Since the historical research on minimizing ESOP expressions is now still active, our protocol will "automatically" turn to an efficient one as this research progresses. Thus, we hope that the existence of our cryptographic protocol would motivate further research on minimizing ESOP expressions.

Minimization of exclusive sum-of-products expressions for multiple-valued input, incompletely specified functions

This paper presents a new operation (exorlink) and an algorithm to minimize Exclusive-OR Sum-of-Products expressions (ESOPs) for multiple valued input, two valued output, incompletely specified functions. Exorlink is a more powerful operation than any other existing one for this problem. Evaluation on benchmark functions is given and it proves the superiority of the program to those known from the literature.

A simplification method for AND‐EXOR expressions for multiple‐output functions

AbstractThis paper presents properties of Exclusive‐OR Sum‐of‐Products expressions (ESOPs) for multiple‐output functions and a simplification algorithm for ESOPs. First, lower bounds on the number of products in minimum ESOPs for multiple output functions are derived. Then, algorithms to simplify ESOPs and to prove their minimality are presented. Experimental results for arithmetic functions and randomly generated functions for up to ten variables are shown.

EXMIN2: a simplification algorithm for exclusive-OR-sum-of-products expressions for multiple-valued-input two-valued-output functions

Minimization of AND-EXOR programmable logic arrays (PLAs) with input decoders corresponds to minimization of the number of products in Exclusive-OR sum-of-products expressions (ESOPs) for multiple-valued-input two-valued-output functions. A simplification algorithm for ESOPs that iteratively reduces the number of the products in ESOPs and then reduces the number of the literals is presented. Various rules are used to replace a pair of products with another one. Many AND-EXOR PLAs for arithmetic circuits have been simplified. In most cases, AND-EXOR PLAs required fewer products than AND-OR PLAs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>