Optimization of Combinational Logic Circuits Using NAND Gates and Genetic Programming

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  author =       "Arezoo Rajaei and Mahboobeh Houshmand and 
                 Modjtaba Rouhani",
  title =        "Optimization of Combinational Logic Circuits Using
                 NAND Gates and Genetic Programming",
  booktitle =    "Soft Computing in Industrial Applications",
  publisher =    "Springer",
  year =         "2011",
  editor =       "Antonio Gaspar-Cunha and Ricardo Takahashi and 
                 Gerald Schaefer and Lino Costa",
  volume =       "96",
  series =       "Advances in Intelligent and Soft Computing",
  pages =        "405--414",
  keywords =     "genetic algorithms, genetic programming",
  isbn13 =       "978-3-642-20504-0",
  DOI =          "doi:10.1007/978-3-642-20505-7_36",
  abstract =     "The design of an optimised logic circuit that
                 implements a desired Boolean function is of interest.
                 Optimisation can be performed in terms of different
                 objectives. They include optimising the number of
                 gates, the number of levels, the number of transistors
                 of the circuit, etc. In this paper, we describe an
                 approach using genetic programming to optimize a given
                 Boolean function concerning the above mentioned
                 objectives. Instead of commonly used set of gates, i.e.
                 {AND, OR, NOT, XOR}, we use the universal NAND gates
                 which lead to a faster and more compact circuit. The
                 traditional gate minimisation techniques produce
                 simplified expressions in the two standard forms: sum
                 of products (SOP) or product of sums (POS). The SOP
                 form can be transformed to a NAND expression by a
                 routine, but the transformation does not lead to
                 optimized circuit; neither in terms of the number of
                 gates, nor the number of levels. Experimental results
                 show our approach produces better results compared to
                 transforming the SOP form to the NAND expression, with
                 respect to the number of gates, levels and transistors
                 of the circuit.",

Genetic Programming entries for Arezoo Rajaei Mahboobeh Houshmand Modjtaba Rouhani