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SELECTION OF SOLUTIONS FOR DESIGNING OPEN SYSTEMS BASED ON ANALYSIS OF VARIANTS WITH RANDOM WEIGHTS
Российский технологический журнал, 2018 A new one-parameter approach to the selection of optimal solutions for the design of complex systems is proposed. The approach is based on the analysis of a tree of variants with random weights (here weight is a certain non-negative quantity: for example,
A. A. Pastushkov, V. K. Batovrin
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, 2013 We introduce and study an abstract class of semirings, which we call exact semirings, defined by a Hahn-Banach-type separation property on modules.
Butkovič +15 more
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Cryptography Based on (Idempotent) Semirings: Abandoning Tropicality?
EncyclopediaThis review explores the current state of public key cryptography based on idempotent semirings, with an emphasis on tropical semirings. It examines key hard problems, such as the tropical discrete logarithm problem, semidirect tropical product problem ...
Mariana Durcheva
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Quantum Algorithms for Matrix Products over Semirings [PDF]
, 2014 19 ...
François Le Gall, Harumichi Nishimura
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MathematicsIn the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging the computational prowess of tropical semirings and the structural resilience of block matrices.
Mariana Durcheva, Kiril Danilchenko
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Algebraic structures of tropical mathematics
, 2013 Tropical mathematics often is defined over an ordered cancellative monoid $\tM$, usually taken to be $(\RR, +)$ or $(\QQ, +)$. Although a rich theory has arisen from this viewpoint, cf.
Izhakian, Zur +2 more
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AxiomsThe explicit forms of idempotent and semicentral idempotent triangular matrices over an additively idempotent semiring are obtained. We define a diamond composition of idempotents and give a representation of an idempotent n×n matrix as an (n−1)th degree
Dimitrinka Vladeva
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Synchronizing weighted automata
, 2014 We introduce two generalizations of synchronizability to automata with transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently, to finite sets of matrices in K^nxn.) Let us call a matrix A location-synchronizing if there exists a ...
Iván, Szabolcs
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Congruence-simple matrix semirings
International Journal of Algebra and ComputationIt is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring [Formula: see text], of all [Formula: see text] matrices over a semiring S, is congruence-simple, provided that either S has a multiplicatively absorbing element or S is ...
Vítězslav Kala +2 more
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The Discrete Lyapunov Equation of The Orthogonal Matrix in Semiring
European Journal of Pure and Applied Mathematics, 2023 Semiring is an algebraic structure of (S, +, ×). Similar to a ring, but without the condition that each element must have an inverse to the adding operation. The forms (S, +) and (S, ×) are semigroups that satisfy the distributive law of multiplication and addition. In matrix theory, there is a term known as the Kronecker product.
Ariyanti, Gregoria +1 more
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