Abstract
In this paper, we intend to introduce a heuristic algorithm to apply maximum minimization to Boolean functions with normal SOP form. To implement the proposed algorithm, we use the graph data structure and define the adjacencies. Also, we demonstrate some conditions to achieve the maximum minimization. Through this paper, the problem of shared vertices in more than one adjacency is talked, and the solution is presented. Also, don’t-care statements are considered and the way of behaving with them is explained. Karnaugh map is used to clarify the matter.
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References
Harris, D.M., Harris, S.L.: Digital Design and Computer Architecture, pp. 51–62. Morgan Kaufmann, San Francisco (2007)
Hlaviča, J., Fišer, P.: A Heuristic Method of Two-Level Logic Synthesis. Karlovo nám 13, 121 35 Prague 2
Mintz, A., Golumbic, M.C.: Factoring Boolean functions using graph partitioning. Discrete Applied Mathematics 149 (2005)
Horowitz, E., Sahni, S., Mehta, D.: Fundamentals of Data Structures in C++, 2nd edn. Silicon Press (2006)
Bondy, J.A., Murty, U.S.R.: Graph theory with applications, 9th edn., pp. 1–24. Elsevier Science Ltd, Amsterdam (1976)
Lipschutz, S.: Schaum’s outline of theory and problems of discrete mathematics, 3rd edn., pp. 154–200. McGraw-Hill, New York (2009)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs, 2nd edn. Annals of Discrete Mathematics, vol. 57. Elsevier, Amsterdam (2004)
Puntambekar, A.A.: Design & Analysis of Algorithms, 1st edn., pp. (6-1)–(6-5). Technical Publications, Pune (2010)
Koffman, E.B., Wolfgang, P.A.T.: Data Structures: Abstraction and Design Using Java, pp. 547–550. John Wiley & Sons, Chichester (2010)
Balch, M.: Complete Digital Design, pp. 3–32. McGraw-Hill, New York (2003)
Popel, D.V.: Information theoretic approach to logic function minimization (ebook). Technical University of Szczecin (2000)
Nelson, V.P.: Digital logic circuit analysis and design, 2nd edn., pp. 90–120. Prentice Hall, Englewood Cliffs (1995)
Sasao, T.: EXMIN2: A Simplification Algorithm for Exclusive-OR-Sum-of -Products Expression for Multiple-Valued-Input Two-Valued-Output functions. IEEE Trans. on Computer Aided Design 12, 621–632 (1993)
Thornton, M.A., Drechsler, R., Miller, D.M.: Spectral Techniques in VLSI CAD. Kluwer Academic Publ., Dordrecht (2001)
Karp, R.M.: Reducibility Among Combinatorial Problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Parberry, I.: Lecture notes on algorithm analysis and computational complexity (ebook). Department of Computer Science, University of North Texas, pp. 66–71
Wang, Y.: Data structures: Minimization and complexity of Boolean functions (ebook). A thesis of Ph.D degree, University of Saskatchewan, Canada, pp. 8–20 (1995)
Bondy, J.A., Murty, U.S.R.: Graduated Texts in Mathematics: Graph theory, pp. 1–8. Springer, Heidelberg (2010)
Vahid, F.: Digital Design with RTL Design, Verilog and VHDL, 2nd edn., pp. 336–337. John Wiley and Sons, Chichester (2010)
Mano, M.M.: Digital Design, 4th edn., pp. 36–110. Prentice Hall, Englewood Cliffs (2006)
He, M., Petoukhov, S.: Mathematics of Bioinformatics: Theory, Methods and Applications, pp. 138–139. Wiley, Chichester (2011)
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Nosrati, M., Karimi, R., Aziztabar, R. (2011). Minimization of Boolean Functions Which Include Don’t-Care Statements, Using Graph Data Structure. In: Al-Majeed, S.S., Hu, CL., Nagamalai, D. (eds) Advances in Wireless, Mobile Networks and Applications. ICCSEA WiMoA 2011 2011. Communications in Computer and Information Science, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21153-9_20
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DOI: https://doi.org/10.1007/978-3-642-21153-9_20
Publisher Name: Springer, Berlin, Heidelberg
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