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A logical function f is AND bi-decomposable if it can be written as f x1, x2)= h1 (x1) h2(x2), where x1 and x2 are disjoint. Such functions are important because they can be efficiently implemented. Also many benchmark functions are AND bi-decomposable. Surprisingly, the minimal sum of products (MSOP) of f is not always obtainable by finding the MSOP of h1 and h2 and applying the law of distributivity. However, a special class of functions called orthodox functions, introduced by Sasao and Butler [1], do have this property. This thesis focuses on orthodox functions, and the remaining non-orthodox functions. It is shown how to build up orthodox functions from orthodox functions on fewer variables. An algorithm is presented for generating families of non-orthodox functions. A test program is developed to test the results of the proposed algorithm and also other programs are developed to conduct experiments with both orthodox and non-orthodox functions. Results are presented that represent the first steps toward completely characterizing bi-decomposable functions that can be efficiently implemented., http://archive.org/details/minimizationofso109456005, Lieutenant Junior Grade, Turkish Navy, Approved for public release; distribution is unlimited.

Minimization is one of the most important issues in logical design. When we decide to develop a circuit to perform a certain task, one of the most important steps is to create this circuit with the minimum number of logical elements, since this reduces the cost, area and latency issues. However, minimization may require too much time, affecting the circuit's cost. There are many minimization tools. Each of them uses a different approach to solve the minimization problem. Considering the speed of the minimization process, those that split the functions into components and minimize each component separately yield the highest efficiency.

A logical function f is AND bi-decomposable if it can be written as f x1, x2)= h1 (x1) h2(x2), where x1 and x2 are disjoint. Such functions are important because they can be efficiently implemented. Also many benchmark functions are AND bi-decomposable. Surprisingly, the minimal sum of products (MSOP) of f is not always obtainable by finding the MSOP of h1 and h2 and applying the law of distributivity. However, a special class of functions called orthodox functions, introduced by Sasao and Butler [1], do have this property. This thesis focuses on orthodox functions, and the remaining non-orthodox functions. It is shown how to build up orthodox functions from orthodox functions on fewer variables. An algorithm is presented for generating families of non-orthodox functions. A test program is developed to test the results of the proposed algorithm and also other programs are developed to conduct experiments with both orthodox and non-orthodox functions. Results are presented that represent the first steps toward completely characterizing bi-decomposable functions that can be efficiently implemented.