Results 1 to 10 of about 109 (103)

The Rényi Entropies Operate in Positive Semifields [PDF]

Entropy, 2019
We set out to demonstrate that the Rényi entropies are better thought of as operating in a type of non-linear semiring called a positive semifield.
Francisco J. Valverde-Albacete, Carmen Peláez-Moreno   +1 more
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Convexity via Weak Distributive Laws [PDF]

Logical Methods in Computer Science, 2022
We study the canonical weak distributive law $\delta$ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields.
Filippo Bonchi, Alessio Santamaria
doaj   +1 more source

Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields

Mathematics, 2021
Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings.
Francisco José Valverde-Albacete, Carmen Peláez-Moreno   +1 more
doaj   +1 more source

Algebraic Solution of Tropical Polynomial Optimization Problems

Mathematics, 2021
We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with idempotent addition and invertible multiplication).
Nikolai Krivulin
doaj   +1 more source

Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons

Mathematics, 2021
We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings.
Nikolai Krivulin
doaj   +1 more source

Hyper-Minimization for Deterministic Weighted Tree Automata [PDF]

Electronic Proceedings in Theoretical Computer Science, 2014
Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided.
Andreas Maletti, Daniel Quernheim
doaj   +1 more source

Algebraic Solution of Tropical Best Approximation Problems

Mathematics, 2023
We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition.
Nikolai Krivulin
doaj   +1 more source

The Singular Value Decomposition over Completed Idempotent Semifields

Mathematics, 2020
In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD).
Francisco J. Valverde-Albacete, Carmen Peláez-Moreno   +1 more
doaj   +1 more source

Pushing for weighted tree automata [PDF]

Logical Methods in Computer Science, 2018
A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it is most useful ...
Thomas Hanneforth, Andreas Maletti, Daniel Quernheim   +2 more
doaj   +1 more source

On the Knuth semi-fields

International Journal of Mathematics and Mathematical Sciences, 1980
We consider three of Knuth's four classes of semi-fields—Knuth [11]—namely, those having dimension 2 over a nucleus and show that the autotopism group is solvable (Corollary 4.12). This generalizes a result of Hughes [5].
D. R. Hughes, M. J. Kallaher
doaj   +1 more source