CONCEPTION OF THE OPTIMAL FORM OF THE LOGICAL FUNCTIONS PRESENTATION AND PROBLEMS OF ITS IMPLEMENTATION

Олена Миколаївна Панаско, Сергій Владиславович Бурмістров

Abstract


In scientific publications and conducted studies, the possibility of representing logical functions (LF) in alternative forms of representation is demonstrated, the characteristic feature of which is a polynomial entity, which reduces to the representation of LF in the form of series different from the traditional classical  representation by adding members of a series - in particular, for an algebraic form, the addition is carried out algebraically with weight coefficients, and in the case of the use of the Reed-Muller form addition is made for mod 2. The results of complete sets of logical functions studies proved that the traditional classical form does not always ensure the minimality of indicators for the structural complexity of  the logical functions implementation, which makes relevant further steps in determining the optimal forms for representing logical functions in the problems of discrete devices analysis and synthesis. The implementation of the combination scheme for a given logical function from n arguments is carried out by some set of variants of structures. In problems of analysis and synthesis of combinational circuits of discrete devices it is necessary to evaluate the quality of their possible structures, to provide identification and selection of the most successful or optimal ones. The concept of the logical functions optimal form of representation is presented in the article as an important direction of structural perfection of discrete devices on the basis of their logical functions realization in alternative forms of representation. The existence of the OFR-concept, which takes into account different forms of representation, makes it highly efficient to use alternative forms of logical functions representation from the point of the structural complexity parameters of the combinational schemes implementation in comparison with traditional classical form. The article outlines the factors for the further improvement of the OFR-concept by filling it with new scientific achievements, which will allow to completely or partially remove difficulties with the introduction of the optimal FR into broad engineering practice

Keywords


logical functions; presentation form; optimal form of representation; indicators of structural complexity of implementation; subsets of priorities; differentiation of logical functions

References


D'yachenko, V. V., Suprun, V. P. Minimizatsiya simmetricheskikh bulevykh funktsii v klasse polinomov Rida – Mallera [Minimization of symmetric Boolean functions in the class of Reed-Muller polynomials]. Dyskretnaya matematyka, alhebra y ykh prylozhenyya: tez. dokl. Mezhdunar. nauch. konf. [International Scientific Conference Discrete mathematics, algebra and their applications]. Mynsk, 2015, pp. 98-100.

Alekseichuk, A. N., Konyushok, S. N. Algebraicheski vyrozhdennye priblizheniya bulevykh funktsii [Algebraically degenerate approximations of Boolean functions]. Kibernetika i sistemnyj analiz, 2014, vol. 50, no. 6, pp. 3-14.

Wang, P., Wang, Z., Xu, R., Jiang, Z., Wang, D. Conversion algorithm for MPRM expansion. Journal of Semiconductor, Institute of Circuits and Systems, Ningbo University, Ningbo, China, 2014, vol. 35, no. 3, pp. 150-155.

He, Z., Xiao L., Ruan, L. A power and area optimization approach of mixed polarity Reed-Muller expression for incompletely specified Boolean functions. Journal of computer science and technology, 2017, vol. 32, no. 2, pp. 297 – 311. doi: 10.1007/s11390-017-1723-1.

Kochkarev, Yu., Kazarinova, N., Panteleeva, N. Klassicheskie i al'ternativnye minimal'nye formy logicheskikh funktsii. Katalog – spravochnik : monografiya [Classical and alternative minimal forms of logical functions]. Institut problem modelirovanija v jenergetike im. G. E. Puhova, Cherkassy, Cherkasskij institut upravlenija Publ., 1999. 195 p.

Kochkarev, Yu. A., Panteleeva, N. N., Kazarinova, N. L. Optimizatsiya struktury tsifrovykh ustroistv s pomoshch'yu ob"edineniya klassicheskikh i neklassicheskikh form [Optimizing the structure of digital devices by combining classical and non-classical forms]. Elektronika i svyaz', 2002, no. 14, pp. 106 – 108.

Kochkarev, Yu. A., Panteleeva, N. N. Dinamika izmeneniya moshchnosti podmnozhestv logicheskikh funktsii, perspektivnykh dlya al'ternativnykh realizatsii [Dynamics of the change in the power of subsets of logical functions that are promising for alternative realizations]. Elektronika i svyaz', 2002, no. 11, pp. 81 – 86.

Kochkarev, Yu. A., Panasko, E. N., Shakun, S. A. Sovershenstvovanie struktury apparatnykh sredstv obrabotki signalov na osnove mul'tiformnogo predstavleniya logicheskikh funktsii [Perfection of the structure of signal processing hardware based on the multiform presentation of logical functions]. Elektronika i svyaz', no. 1, 2006, pp. 82 - 86.

Kochkarev, Yu. A., Panasko, E. N., Kucherova, N. S. Statisticheskaya otsenka poter' ot neoptimal'nosti formy predstavleniya logicheskikh funktsii [Statistical estimation of losses from non-optimal form of representation of logical functions]. Zbirnyk naukovykh prats' Natsional'noho hirnychoho universytetu, Dnipropetrovsk, 2009, no. 32, pp. 171-177.

Kochkarev, Yu. A., Panasko, E. N. Otsenka effektivnosti primeneniya porazryadnogo invertirovaniya vkhodnykh peremennykh pri optimizatsii struktury tsifrovykh blokov [Estimation of the efficiency of application of bitwise inverting of input variables while optimizing the structure of digital blocks]. Prikladnaya radioelektronika, 2010, vol. 9, no. 2, pp. 295-297.

Kochkarev, Y. A., Osipenkova, I. I., Panasko, E. N. Ortogonal forms of presentation of boolean functions in device blocks. Datchiki, pribory i sistemy DPS – 2009 : materialy mezhdunarodnoj nauchno-tehnicheskoj konferencii, Yalta, 2009, pp. 39-42.

Kochkarev, Yu. A., Panasko, E. N., Sin'ko, I. V. Vozmozhnosti realizatsii logicheskikh funktsii v ortogonal'noi forme predstav-leniya [The possibilities of implementing logical functions in the orthogonal form of representation]. Visnyk Cherkas'koho derzhavnoho tekhnolohichnoho universytetu. Cherkasy, ChDTU Publ., 2011, no. 1, pp. 45 - 49.

Panasko, O. M. Doslidzhennya efektyvnosti ortohonal'noyi formy predstavlennya lohichnykh funktsiy [Doslіdzhenny efektivnosti orthogonalnogo form represented by logistic functions]. Visnyk Cherkas'koho derzhavnoho tekhnolohichnoho universytetu, Cherkasy, ChDTU Publ., 2013, no. 4, pp. 7 − 13.

Panasko, O. M. Poshuk odnakovykh frahmentiv pry minimizatsiyi lohichnykh funktsiy v ortohonal'niy realizatsiyi [Search of identical fragments at minimization of logical functions in the orthogonal implementation]. Radioelektronni i komp'uterni sistemi - Radioelectronic and computer systems, 2014, no. 1 (65), pp. 92 –97.




DOI: https://doi.org/10.32620/reks.2018.1.04

Refbacks

  • There are currently no refbacks.