Efficient and Simultaneous Computation of  Logic Expressions with Memorizing Intermediate Computations

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Rahgoshay, Mirmahdi | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48146 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Abam, Mohammad Ali
Abstract:
The Minimization of multi output Boolean functions is a fundamental and classic problem in logical circuits. For single output functions Karnough Map and Quine-McCluskey algorithms are the most common ways; however, for multi output functions they can be used to every output, but it does not necessary give the optimal solution. In this thesis we are going to compute simple expressions (expression in which we have just one type of operators) with minimum operations. We assume that we can use intermediate results in calculating other expressions to reduce repeated operations. In this thesis, first we compare the optimal solution of ‘and’ and ‘or’ operator with the ‘xor’ operator, and after proof of the hardness of the problem of concurrent minimization of simple logical expressions with ‘or’ and ‘and’ operator for k=3 by using the reduction of ‘Vertex Cover’ problem, we would prove the hardness of the problem for ‘xor’ operator. Finally we provide an approximation algorithm with a constant factor for the simple expressions with these operators for k=3
Keywords:
Logical Expressions ; Operator Minimization ; Gate Minimization

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