Efficient Algorithm and Implementation for Boole Reduction of Large Logic Expressions

Boolean algebra, introduced in the 19th century by the mathematician, philosopher, and logician George Boole, has been foundational in mathematics, logic, computer science, machine proofs, and digital electronics. Recently, a new framework, the “Algebra of Boole,” proposed by Professor Norman J. Wildberger, offers a more natural and powerful alternative. To apply this new framework to important areas, such as artificial intelligence, complex machine proofs, and large-scale circuit designs, it is essential to develop a method for automatically reducing complicated logic expressions into a simple standard form. This paper is on developing an efficient algorithm and implementation for Boole Reduction, a process that simplifies large logic and Boole expressions into compact, canonical forms. By utilizing Key Boole Properties from the Algebra of Boole, the algorithm processes arbitrarily complex logic expressions, reducing them iteratively to a canonical form through sophisticated reduction techniques until no further simplifications are possible. Expressions with varying complexity, from simple binary operations to large multi-variable expressions, are used to test the algorithm. Results show a significant improvement in reduction speed and computational efficiency compared to brute-force methods, demonstrating the algorithm’s feasibility in handling complex logic expressions. One of the aims of this work is also to stimulate research in the framework of the Algebra of Boole as well as its applications in areas such as propositional logic, AI reasoning, and the optimization of digital circuit designs.