Binary Representations of Algebras With at Most Two Binary Operations: A Cayley Theorem for Distributive Lattices

Movsisyan, Yu. M.

doi:10.1142/s0218196709004993

Cited by 22 publications

(3 citation statements)

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“…Some recent papers discussing different properties, new directions in development of hyperidentities and applications are discussed in [5,6,7,12,13,16]. A discussion about hyperidentities in distributive lattices is given in [12]. The application of hyperidentities for reducing the complexity of switching circuits is discussed in [7].…”

Section: Definition 23mentioning

confidence: 99%

Circuit Integration Through Lattice Hyperterms

Melkonian

2011

Discrete Math. Algorithm. Appl.

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Reducing the size of a logic circuit through lattice identities is an important and well-studied discrete optimization problem. In this paper, we consider a related problem of integrating several circuits into a single hypercircuit using the recently developed concept of lattice hyperterms. We give a combinatorial algorithm for integrating k-out-of-n symmetrical diagrams which play an important role in reliability theory. Our results show that the integration can reduce the number of circuit gates by more than twice.

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Section: Definition 23mentioning

confidence: 99%

Circuit Integration Through Lattice Hyperterms

Melkonian

2011

Discrete Math. Algorithm. Appl.

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“…where x = (x) [2,3,5,4,6,16,[25][26][27]11,23,32]. The standard fuzzy algebra F = ([0, 1]; max(x, y), min(x, y), 1 − x, 0, 1) is an example of a De Morgan algebra.…”

Section: Introductionmentioning

confidence: 99%

A functional completeness theorem for De Morgan functions

Movsisyan

Aslanyan

2014

Discrete Applied Mathematics

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Available online xxxx Keywords: Antichain De Morgan function Monotone Boolean function Disjunctive (conjunctive) normal form of De Morgan function Closed class Complete and precomplete classes Quasimonotone and zigzag De Morgan functions a b s t r a c tIn this paper we define disjunctive and conjunctive normal forms of De Morgan functions and prove a functional completeness theorem for these functions.

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“…Algebras of binary functions with these operations were also studied in [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Assume that L = (L; +, •, 0, 1) is a bounded distributive lattice.…”

Section: Introductionmentioning

confidence: 99%

Characterization of binary polynomials of idempotent algebras

Movsisyan

Pashazadeh

2012

J Math Sci

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In this paper, we characterize the set of all binary algebraic (or polynomial) operations of an idempotent algebra that has at least one r-ary algebraic operation, (r ≥ 2), depending on every variable such that there is no an (r + 2)-ary algebraic operation depending on at least (r + 1) variables. We prove that this set forms a finite Boolean algebra, and then we characterize this Boolean algebra.

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Binary Representations of Algebras With at Most Two Binary Operations: A Cayley Theorem for Distributive Lattices

Cited by 22 publications

References 21 publications

Circuit Integration Through Lattice Hyperterms

Circuit Integration Through Lattice Hyperterms

A functional completeness theorem for De Morgan functions

Characterization of binary polynomials of idempotent algebras

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