Abstract
A new method of coding minorants in decomposing a system of Boolean function is proposed. The method is based on the initial coding obtained from the minimal representation of the system in the so-called set-theoretical decomposition form obtained as a result of q-partitioning of conjuncterms of functions represented in DNF. A distinctive feature of the method is the preservation of the correspondence of the obtained codes of minorants to the block structure of the system being decomposed, which provides the minimum of informational capacity of PLAs.
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REFERENCES
H. A. Curtis, A New Approach to the Design of Switching Circuits, Princeton (N.J.), Toronto (1962).
M. A. Rakov (ed)., A. B. Kmet, A. L. Lantsov, et al., Specialized Multiple-Valued Analyzers [in Russian], Naukova Dumka, Kiev (1977).
A. D. Zakrevskii, Logic Synthesis of Cascade Circuits [in Russian], Nauka, Moscow (1981).
P. N. Bibilo and S. V. Yenin, Synthesis of Combinational Circuits by Methods of Functional Decomposition [in Russian], Nauka i Tekhnika, Minsk (1987).
P. N. Bibilo, Synthesis of Combinational PLA-Structures for VLSI Circuits [in Russian], Navuka i Tekhnika, Minsk (1992).
V. A. Mishchenko (ed.), Logic Design of LSI Circuits [in Russian], Radio and Svyaz', Moscow (1984).
R. K. Brayton, G. D. Hachtel, and A. L. Sangiovanni-Vincentelli, “Multilevel logic synthesis,” Proc. IEEE, 78, No. 2, 264-300 (1990).
Ye. S. Bul', “Combined implementation of systems of switching functions by a PLA-based circuit,” AVT, No. 3, 36-41 (1981).
B. Ye. Rytsar, “A new approach to the decomposition of Boolean functions by the method of 2-partitions. 1. Separating decomposition of full and partial functions,” Kibern. Sist. Analiz, No. 5, 38-62 (2001).
B. Ye. Rytsar, “A new approach to the decomposition of Boolean functions by the method of q-partitions. II. Repeated decomposition,” Kibern. Sist. Analiz, No. 1, 54-63 (2002).
I. P. Suprun, “A Method of PLA-based implementation of Boolean functions specified in interval form,” AVT, No. 5, 30-36 (1982).
T. Sasao, “Application of multivalued logic to a serial decomposition of PLAs,” in: Proc. 19th ISMVL (Guangzhou, China), IEEE, New York (1989), pp. 264-271.
T. Sasao, Logic Synthesis and Optimization, Kluwer Academic, Boston-London-Dordrecht (1993).
R. Murgai, R. K. Brayton, and A. L. Sangiovanni-Vincentelli, “Optimal functional decomposition using encoding,” in: Proc. 31th ACM/IEEE DAC (1994), pp. 408-414.
M. Rawski, L. Jozwiak, and T. Luba, “The influence of the number of values in subfunctions on the effectiveness and efficiency of the functional decomposition,” in: Proc. 25th EUROMicro Conf. (Milan, Italy) (1999), pp. 86-93.
A. Chojnacki and L. Jozwiak, “Multivalued subfunction encoding in functional decomposition based on information relationships measures,” in: Proc. 30th ISMVL (Portland, Oregon), IEEE, New York (2000), pp. 21-28.
B. Ye. Rytsar, “Functional decomposition in the class of DNFs by the method of q-partitions of conjuncterms,”Visnyk NU “L'vivs'ka Politekhnika,” Computer Engineering and Information Technologies, No. 433, 212-225 (2001).
B. Ye. Rytsar, “A method of minimization of Boolean functions,” Probl. Upravlen. Inf., No. 2, 100-113 (1997).
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Rytsar, B.Y., Kmet', A.B. A New Method of Coding Minorants in Problems of Synthesis of Digital Devices from PLAs. Cybernetics and Systems Analysis 39, 212–234 (2003). https://doi.org/10.1023/A:1024787122371
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DOI: https://doi.org/10.1023/A:1024787122371