準教授　Grant Pogosyan

最近の研究活動

  1. Algebra of multiple-valued logic.
    The lattice of clones of multiple-valued logic functions has been studied further. For the logics of arities at least 3, the lattice in question is still largely unknown. The focus in the current research is shifted towards the bottom (atomic) part of the lattice. New results have been obtained for the so-called join-irreducible clones, i.e. clones that can't be expressed through others using the lattice join operation.

  2. Complexity and formal representations of logic functions.
    Orthogonal expansions of logic functions. The notions of orthogonal expansion, orthogonal rank, ortho-linearity are introduced for the logic functions. This is a new approach to study the complexity and expressability problems of finite-valued functions.
    Efficiently irreducible generating sets. A new notion of the efficient base of operations has been introduced. It is a set of generators in multiple-valued logic, that is irreducible without loss of complexity of expressions. The goal of the research was to completely describe and enumerate all the efficient bases of boolean and ternary logic functions.

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研究論文

  1. Pogosyan, G., Nozaki, A.: Join-irreducible clones of multiple-valued logic algebra, Proceedings 25th International Symposium on Multiple Valued Logic, Bloomington, Indiana, U.S.A., May 1995, 194-199, IEEE Press.

  2. Pogosyan, G.: Tachironri kansu no chokko tenkai ni tsuite (On orthogonal expansion of logic functions), Note on Multiple-Valued Logic in Japan, 17(16), 1-8 (1995).

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研究発表

  1. Join-irreducible clones of multiple-valued logic algebra, 25th International Symposium on Multiple Valued Logic, Bloomington, Indiana, U.S.A., May 1995.

  2. Tachironri kansu no chokko tenkai ni tsuite, Tachironri Forum, Shizuoka, 1995.

  3. Closed classes of logic functions under compositions with feedback loops, International Conference "Intelligent Systems and Computer Science", Moscow State University, Moscow, Russia, November 1995.

  4. Efficiently irreducible generating sets of logic functions, International Conference "Intelligent Systems and Computer Science", Moscow State University, Moscow, Russia, November 1995.

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