Abstract
The problem of implementing Boolean functions in polynomial forms finds applications in the synthesis of logic circuits, in discrete models of system biology. One of the classes of polynomial forms is the class pseudopolynomial forms (PSPF) - expressions that are the sum over modulo two of conjunctions of Zhegalkin polynomials of linear functions. Latest years, the properties of the implementation of Boolean functions in the class have been actively studied PSPF. One of the complexity characteristics of implementing functions in a class psf is the length - the minimum number of terms among all SSPFs that implement the function. The report will present the results of evaluation of the lengths of the system of adder functions and comparator functions in the class PSPF.
Publisher
Keldysh Institute of Applied Mathematics
Reference7 articles.
1. Sasao T., Besslich P. On the complexity of mod-2 sum PLA’s // IEEE Trans. on Comput. 1990. V. 39, No 2. P. 262–266.
2. Veliz-Cuba A., Jarrah A.S., Laubenbacher R. Polynomial algebra of discrete models in systems biology // Bioinformatics. 2010. V. 26, No 13. P. 1637–1643.
3. Hinkelmann F., Brandon M., Guang B., McNeill R., Blekherman G., Veliz-Cuba A., Laubenbacher R. ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra // BMC Bioinformatics. 2011. V. 12, No 1. P. 295.
4. Elmeligy Abdelhamid S.H., Kuhlman C.J., Marathe M.V., Mortveit H.S., Ravi S.S. GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems // PLoS ONE. 2010. V. 10, No 8. P. 1–24.
5. Ishikawa R., Hirayama T., Koda G., Shimizu K. New three-level Boolean expression based on EXOR gates // IEICE Trans. Inf. & Syst. 2004. V. 87-D No 5. P. 1214–1222.