.png){kind=icon}
.png){kind=icon}
Return
Novel Boolean logic manipulation : A symbolic computation and camouflaged graph construction
.png){kind=icon}
PRE
AI
DOI：10.47974/jios-2220.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This article introduces a systematic, symbolic, and pure algebraic technique called the "Extraction and Combination Method" for minimizing Boolean expressions. This method simplifies Boolean expressions through a sequence of algebraic manipulations that methodically extract factors and combine terms to reduce the complexity of redundant literal terms and operations. The algorithmic process involves the breakdown of the complex Boolean expression into distinct components, applying the natural and fundamental laws of Boolean algebra. Systematic ordering and generalization of Boolean operations/ subexpressions ensure that we can invariably reach termination and achieve a unique minimized form for any given Boolean expression. The set of processes of decomposition of the expression into subexpressions, parallel minimization, and recombination is repeated iteratively until we get an optimized form. The minimization process avoids exhaustive truth table generation. We proposed to seamlessly transform the algebraic form used in our framework into a Boolean graph-a simple undirected graph in the graph-theoretic sense that allows Boolean expressions to be studied and manipulated through graph operations such as union and intersection, and establishes a natural bridge between algebraic logic and classical graph theory. The method enables tautology detection, construction of Boolean graph and camouflaged graph, identification and removal of auxiliary vertices and auxiliary subgraphs, and derivation of simplified Boolean graphs representing minimal expressions.
Keywords:
Boolean graph
Algebraic graph theory
Tautology
Simplification
Obfuscation
Logic minimization
Journal
J
IF:
0.7
Papers:
128
Citations:
0
View more organizations