Abstract
This paper deals with the synthesis of combinatorial circuits by decomposition. The main idea of each decomposition method is that a complicate Boolean function is split into two or more simpler subfunctions. In this way the trivial function f = x i can be achieved after a certain number of decomposition steps and terminates the decomposition procedure.
The two subfunctions of a bi-decomposition are simpler than the given function because the number of independent variables is reduced at least by one. However, for completeness, the weak bi-decomposition is needed, in which only one of the two subfunctions depends on less variables than the given function.
The main aim of this paper is to answer the question whether further subfunctions for a bi-decomposition exist which depend on the same number of variables as the given function to decompose, but are simpler regarding a certain measure and allow us to determine simple circuit structures.
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References
Bochmann, D., Dresig, F., and Steinbach, B.: A New Decomposition Method for Multilevel Circuit Design. European Design Automation Conference, Amsterdam, The Netherlands, 1991, pp. 374–377.
Le, T.Q. Testbarkeit kombinatorischer Schaltungen—Theorie und Entwurf (in German). Dissertation thesis, Technical University Karl-Marx-Stadt, Karl-Marx-Stadt, Germany, 1989.
Mishchenko, A., Steinbach, B., and Perkowski, M.: An Algorithm for Bi-Decomposition of Logic Functions. in: Proceedings of the 38th Design Automation Conference 2001. June 18-22, 2001, Las Vegas (Nevada), USA, 2001, pp. 103–108.
Posthoff, Ch. and Steinbach, B.: Logic Functions and Equations - Binary Models for Computer Science. Springer, Dordrecht, The Netherlands, 2004.
Steinbach, B.: Generalized Lattices of Boolean Functions Utilized for Derivative Operations. in: Materiały konferencyjne KNWS’13, Łagów, Poland, 2013, pp. 1–17.
Steinbach, B. and Mishchenko, A.: SNF: A Special Normal Form for ESOPs. in: Proceedings of the 5th International Workshop on Application of the Reed-Muller Expansion in Circuit Design (RM 2001), August 10–11, 2001, Mississippi State University, Starkville (Mississippi), USA, 2001, pp. 66–81.
Steinbach, B. and Posthoff, Ch.: Derivative Operations for Lattices of Boolean Functions. in: Proceedings Reed-Muller Workshop 2013, Toyama, Japan, 2013, pp. 110–119.
Steinbach, B. and De Vos, A.: The Shape of the SNF as a Source of Information. in: Steinbach, B. (Ed.): Boolean Problems, Proceedings of the 8th International Workshops on Boolean Problems, September 18–19, 2008, Freiberg University of Mining and Technology, Freiberg, Germany, 2008, pp. 127–136.
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Steinbach, B. (2015). Simpler Functions for Decompositions. In: Selvaraj, H., Zydek, D., Chmaj, G. (eds) Progress in Systems Engineering. Advances in Intelligent Systems and Computing, vol 366. Springer, Cham. https://doi.org/10.1007/978-3-319-08422-0_119
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DOI: https://doi.org/10.1007/978-3-319-08422-0_119
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