Control Systems and Computers

UDC 519.718

 

A new minimization method of the variables number in complete and incomplete logic functions, based on the procedure of conjunc terms splitting is proposed. The advantages of the proposed method are illustrated by examples of determining nonessential variables in the functions, which are borrowed from the well-known publications.

 

 

 Download full text! (On English)

 

1. Thayse, A., 1980. Boolean Differential Calculus. Germany, Heidelberg: Springer-Verlag, 1980. 367 p.
2. Steinbach, B., Posthoff, C., 2010. “Boolean Differential Calculus”. in: Sasao, T. and Butler, T. Progress in Application of Boolean Functions, Morgan & Claypool Publishers, San Rafael, CA, USA, pp. 55–78, 121–126.
3. Astola, J.T., Stankovic, R.S., 2006. “Fundamentals of Switching Theory and Logic Design”. Springer, 235–250.
4. Zakrevsky, A.D., Pottosin, YU.V., Cheremisinova, L.D., 2007. “The logical basis of the design of discrete devices”. M .: Fizmatlit, 592 p.
5. Yanushkevich, S., Bochmann, D. Stankovic R. et al., 2000. “Logic Differential Calculus: Achievements, Trends and Applications”. Avtomatika and Telemechanika, 6, pp. 155–170. (In Russian).
6. Levashenko, V., Shmerko, V., Yanushkevich, S., Solution of Boolean Differential Equations on Systolic Arrays. Cybernetics and System Analysis, 32 (1), pp. 36–53.
   https://doi.org/10.1007/BF02366579
7. Bochmann, D., Posthoff, CH., Shmerko V. et al., 2000. “Logic Differential Calculus as Part of Switching Theory”. IEE 4-th Int. Conf. on New Inform. Technol. in Educ. NITE’2000, Minsk, Belarus, pp. 126–135.
8. Yanushkevich, S.N. Matrix and Combinatorics Solution of Boolean Differential Equations. Discrete Applied Mathematics, Preprint submitted to Elsevier Preprint, 2001.
9. Sellers, F.F., Hsiao, M.Y., Bearson, L.W., 1968. “Analizing errors with the Boolean difference”. IEEE Trans. Comp, 1, pp. 676–683.
   https://doi.org/10.1109/TC.1968.227417
10. Marinos, P., 1981. “Derivation of minimal complete sets of test-input sequences using Boolean differences”. IEEE Trans. Computers, 20 (1), pp. 25–32.
    https://doi.org/10.1109/T-C.1971.223077
11. Steinbach, B., Zhang, Z., Lang, Ch., 1997. “Logical design of fully testable large circuits by decomposition”. Int. Conf. On Computers-Aided Design of Discrete Devices. Minsk. Belarus, pp. 7–14.
12. Jaakko, T.A., Stankovic, R.S., 2006. Fundamentals of Switching Theory and Logic Design. A Hands on Approach. Springer, 342 p.
13. Yanushkevich, S., 1997. “Matrix method to solve logic differential equations”. Computers and Digital Technique (UK), 144 (5), pp. 267–272.
14. Marincovic, S., Tosic, Z., 1974. “Algorithm for minimal polarized form determination”. IEEE Trans. Computers, 23 (12), pp. 1313–1315.
    https://doi.org/10.1109/T-C.1974.223854
15. Davio, M., Deschamps, J., 1972. “Symmetric discrete functions”. Philips Res. Repts., 27 (5), pp P. 405–445.
16. Suprun, V.P., 1985. “Polynomial decomposition of symmetric Boolean functions’. Izdatelstvo Academy of Sciences of the USSR. cybernetics, 5, pp. 123–127.
17. Yanushkevich, S.N., 1998. “Logic differential calculus in multivalued logic design”. Tech. University of Szczecin Akad. Publ., Poland., pp. 32–39.
18. Zaitseva, E.N., 1993. “Applications of Logic Differential Calculus in CAD of Integrated Circuits”, PhD Thesis, Univ. of Informatics and Radioelectronics, Minsk, Belarus, pp. 45–59. (In Russian).
19. Gorbatov, V.A., 1986. Basics of discrete mathematics. M .: Higher. school., 311 p.
20. Rytsar, B., 2013. “A simple visual method for determining the logical derivatives of arbitrary orders”. Selection and processing of information, 38(114), pp. 125–132.
21. Steinbach, B., Posthoff, C., 2009. Logic Functions and Equations. Examples and Exercises. Springer Science + Business Media B.V., 230 p.
22. Rytsar, B., Romanowski, P., Shvay, A., 2010. “Set-theoretical Constructions of Boolean Functions and theirs Appl. in Logic Synthesis”., 99 (3), pp. 339–354.
23. Rytsar, B.Ye., 2013. “A Numeric Set-Theoretical Interpretation of Polynomial Zhegalkin”, 1, pp. 11-26. (In Russian).
24. Rytsar, B.E.,2013. “A Numeric Set-Theoretical Interpretation of Reed-Muller Expressions with Fixed and Mixed Polarity”, Upravlâûŝie sistemy i mašiny, 3, pp. 30-44. (In Russian).
25. Butler, J.T., Sasao, T., 2010. “Boolean Functions for Cryptography”. Progress in Appl. of Boolean Functions, pp. 33–53.
26. Schneeweiss, W.G., 1989. “Boolean Functions with Engineering Applications and Computer Programs, 264 p.
    https://doi.org/10.1007/978-3-642-45638-1