On the enumeration of rigid hypercompositional structures

Massouros, Christos G.

doi:10.1063/1.4912960

Cited by 11 publications

(15 citation statements)

References 15 publications

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“…For example, we can look for all dependencies whose length exceeds the maximum of lengths of two given dependencies, or all dependencies such that the cardinality of their impact sets is greater than the minimum of the cardinalities of the impact sets of two given dependencies, etc. This technique is similar to the one employed, e.g., in Chvalina [20], Chapter 6 or Massouros and Mittas [18] in the theory of automata, where lengths of compound words were studied from this perspective. Notice also that Al Tahan and Davvaz [32] used this technique to construct cyclic hypergroups of an arbitrary braid group of n brands.…”

Section: Discussionmentioning

confidence: 99%

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Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

2019

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The aim of this paper is to study, from an algebraic point of view, the properties of interdependencies between sets of elements (i.e., pieces of secrets, atmospheric variables, etc.) that appear in various natural models, by using the algebraic hyperstructure theory. Starting from specific examples, we first define the relation of dependence and study its properties, and then, we construct various hyperoperations based on this relation. We prove that two of the associated hypergroupoids are H v -groups, while the other two are, in some particular cases, only partial hypergroupoids. Besides, the extensivity and idempotence property are studied and related to the cyclicity. The second goal of our paper is to provide a new interpretation of the dependence relation by using elements of the theory of algebraic hyperstructures.

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Section: Discussionmentioning

confidence: 99%

“…However, such a case is trivial and not interesting for our purposes. Recall that Massouros and Mittas [18,19] called such hypergroups B-hypergroups, where B stands for binary, while Chvalina [9,20] called them minimal extensive hypergroups. They have been recently used also in the study of breakable semihypergroups [21].…”

Section: Remarkmentioning

confidence: 99%

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

2019

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“…Not to be missed are results concerning the theory of automata collected in Chvalina and Chvalinová [25]. It should be stressed that these results were motivated by Comer [26] and Massouros and Mittas [27].…”

Section: Mathematical Background Of the Modelmentioning

confidence: 99%

Elements of Hyperstructure Theory in UWSN Design and Data Aggregation

2019

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In our paper we discuss how elements of algebraic hyperstructure theory can be used in the context of underwater wireless sensor networks (UWSN). We present a mathematical model which makes use of the fact that when deploying nodes or operating the network we, from the mathematical point of view, regard an operation (or a hyperoperation) and a binary relation. In this part of the paper we relate our context to already existing topics of the algebraic hyperstructure theory such as quasi-order hypergroups, E L -hyperstructures, or ordered hyperstructures. Furthermore, we make use of the theory of quasi-automata (or rather, semiautomata) to relate the process of UWSN data aggregation to the existing algebraic theory of quasi-automata and their hyperstructure generalization. We show that the process of data aggregation can be seen as an automaton, or rather its hyperstructure generalization, with states representing stages of the data aggregation process of cluster protocols and describing available/used memory capacity of the network.

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“…In [14][15][16][17][18][19] it has been shown by G. Massouros, that the set of the states of an automaton, equipped with different hypercompositions, can be endowed with the structure of the hypergroup. The hypergroups that have derived in this way were named attached hypergroups to the automaton.…”

Section: The Path Hypercompositions In Automatamentioning

confidence: 99%

“…G. G. Massouros [14][15][16][17][18] and after him J. Chvalina [1] studied hypergroups associated with automata. Moreover, in [15] G. G. Massouros introduced the path hypercomposition in graphs and subsequently Ch.…”

Section: A(bc) = (Ab)c For Every Abc H (Associativity)mentioning

confidence: 99%

On path hypercompositions in graphs and automata

Massouros¹

2016

MATEC Web of Conferences

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Abstract. The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.

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On the enumeration of rigid hypercompositional structures

Cited by 11 publications

References 15 publications

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Elements of Hyperstructure Theory in UWSN Design and Data Aggregation

On path hypercompositions in graphs and automata

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