Equations In Boolean Algebra Research Articles

Transformation Method for Solving System of Boolean Algebraic Equations

In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n-dimensional cube Kn with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in Kn is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined.

Solution of equations in Boolean algebra

The explicit form of solutions of Boolean equations with one unknown is obtained. The effectiveness of the method is demonstrated for a number of equations whose solution previously has been found only in “tabular” form. The proposed approach leads to a method for solving systems of equations in Boolean set algebra. We use it to analyze the famous paradoxes of set theory, such as the barber paradox and the liar paradox, as well as Russell's and Cantor's paradoxes.

Optimisation of Montgomery modular multiplicationalgorithm for systolic arrays

An improved systolic array for the Montgomery modular multiplication algorithm is presented. The recursive equation proposed by Walter is explicitly transformed into Boolean algebraic equations. By analysing and optimising these equations, the improved systolic array can be made 20% faster than that proposed by Walter.

Some Topics in Code Optimization

Many compilers for higher order languages attempt to translate the source code into “good” object code. Cocke and Schwartz have described an algorithm for discovering when the computation of an expression is redundant (common), and when it can be moved to a less frequently executed region of the program. The present paper includes a tutorial presentation of their basic methods, along with a number of improvements and extensions. These include simplification of the solution method, to save a pass; extension of it to treat the safety constraint, handle multi-entry regions directly, detect additional commonality and code motion after unsafe code motion, and decide where moved code should be put; and combination of the algorithms for commonality and the dead condition, making use of important work of Ken Kennedy. The methods here applied to collecting information for use in code optimization include general algorithms for solving a set of linear equations in Boolean algebra. The algorithms are most useful when the coefficient matrix is sparse.

The Logical Design of a Simple General Purpose Computer

The logical design described here is used in MINAC, partially constructed at the California Institute of Technology, and LGP-30, manufactured by Librascope Inc. These serial binary digital computers make use of magnetic drum bulk storage and use three circulating registers and fifteen flip-flops. The procedures used in performing the sixteen elementary operations are described. These descriptions indicate the circumstances in which each flip-flop or circulating register input is activated. The Boolean algebraic equations summarizing these circumstances constitute the logical design.

J. A. Postley. A method for the evaluation of a system of Boolean algebraic equations. Mathematical tables and other aids to computation, vol. 9 (1955), pp. 5–8.

J. A. Postley. A method for the evaluation of a system of Boolean algebraic equations. Mathematical tables and other aids to computation, vol. 9 (1955), pp. 5–8.

A Method for the Evaluation of a System of Boolean Algebraic Equations

A Method for the Evaluation of a System of Boolean Algebraic Equations

A method for the evaluation of a system of Boolean algebraic equations

A method for the evaluation of a system of Boolean algebraic equations