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Boolean function minimization in the class of disjunctive normal forms

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Abstract

The survey focuses on minimization of boolean functions in the class of disjunctive normal forms (d.n.f.s) and covers the publications from 1953 to 1986. The main emphasis is on the mathematical direction of research in boolean function minimization: bounds of parameters of boolean functions and algorithmic difficulties of minimal d.n.f. synthesis). The survey also presents a classification of minimization algorithms and gives some examples of minimization heuristics with their efficiency bounds.

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Literature cited

Publications in Russian and Russian translations

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  82. 82.

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  87. 87.

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  90. 90.

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  91. 91.

    G. F. Losev, “The best local algorithm of index 1 for constructing the sum of irredundant d.n.f.s of a boolean function,” Dokl. AN SSSR,212, No. 4, 816–817 (1973).

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    S. P. Matsyulyavichus, “Matrix method of boolean function minimization,” in: Problems of Computer Logic Design [in Russian], Part 1, Vil'nyus (1974), pp. 86–91.

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    S. S. Medvedev, “8-ary charts for boolean function minimization,” Automata Theory, Seminar [in Russian], No. 1, Kiev (1966), pp. 54–69.

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    L. Mikheeva and Kh. Salum, “Construction of reduced d.n.f. by the method of masks,” Izv. AN EstSSR, Fiz., Mat.,18, No. 4, 458–460 (1969).

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    R. V. Mozharov, “On statistical study of minimization of boolean functions,” in: Discrete Analysis [in Russian], No. 5, Novosibirsk (1965), pp. 31–33.

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    R. V. Mozharov, “A study of minimization of random boolean functions,” Trudy Moskovsk. Inst. Inzh. Zh.-D. Transporta, No. 209, 182–183 (1965).

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    R. G. Nigmatullin, “On variation of complexity of shortest disjunctive normal form on unit sphere,” in: Discrete Analysis [in Russian], No. 6, Novosibirsk (1966), pp. 69–80.

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Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 25, pp. 68–116, 1987.

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Sapozhenko, A.A., Chukhrov, I.P. Boolean function minimization in the class of disjunctive normal forms. J Math Sci 46, 2021–2052 (1989). https://doi.org/10.1007/BF01096022

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Keywords

  • Normal Form
  • Boolean Function
  • Function Minimization
  • Minimization Algorithm
  • Main Emphasis