On path hypercompositions in graphs and automata

Massouros, Christos G.

doi:10.1051/matecconf/20164105003

Cited by 10 publications

(4 citation statements)

References 10 publications

(5 reference statements)

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“…Thus, a join space is a commutative hypergroup satisfying the transposition axiom, and it has applications also in graph theory, automata theory, formal languages, etc. A hyperoperation is called extensive [9,10] (or closed [11]) if the result of the hypercomposition of two elements always contains both elements, i.e., a, b ∈ a • b for any a, b ∈ H. This aspect has been recently re-considered and studied in detail by Massouros et al [12]. Notice that the reproduction axiom is an important consequence of the extensive property, i.e., any extensive hypergroupoid is a quasi-hypergroup.…”

Section: Preliminaries and Notations In Hyperstructure Theorymentioning

confidence: 99%

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: Preliminaries and Notations In Hyperstructure Theorymentioning

confidence: 99%

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

2019

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“…Before including some examples of cyclic hypergroups, recall three very useful lemmas. Notice that, in the following definition, the name "extensive" is used e.g., by Chvalina [24,25] while e.g., Massouros [26] uses a geometrically motivated name "closed". Definition 9.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Cyclicity in EL–Hypergroups

2018

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In the algebra of single-valued structures, cyclicity is one of the fundamental properties of groups. Therefore, it is natural to study it also in the algebra of multivalued structures (algebraic hyperstructure theory). However, when one considers the nature of generalizing this property, at least two (or rather three) approaches seem natural. Historically, all of these had been introduced and studied by 1990. However, since most of the results had originally been published in journals without proper international impact and later—without the possibility to include proper background and context-synthetized in books, the current way of treating the concept of cyclicity in the algebraic hyperstructure theory is often rather confusing. Therefore, we start our paper with a rather long introduction giving an overview and motivation of existing approaches to the cyclicity in algebraic hyperstructures. In the second part of our paper, we relate these to E L -hyperstructures, a broad class of algebraic hyperstructures constructed from (pre)ordered (semi)groups, which were defined and started to be studied much later than sources discussed in the introduction were published.

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“…There followed more papers by the same author and Ch. Massouros, e.g., [13][14][15][16][17][18][19][20][21], as well as other researchers such as J. Chvalina [22][23][24][25][26][27][28], L. Chvalinová [22], Š. Hošková-Mayerová [24,25], M. Novák [26][27][28][29][30][31][32], S. Křehlík [26,27,[29][30][31]33], M.M. Zahedi [34], M. Ghorani [34,35], D. Heidari and S. Doostali [36], R.A. Borzooei et al [37].…”

Section: Introductionmentioning

confidence: 99%

State Machines and Hypergroups

Massouros

2022

Mathematics

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State machines are a type of mathematical modeling tool that is commonly used to investigate how a system interacts with its surroundings. The system is thought to be made up of discrete states that change in response to external inputs. The state machines whose environment is a two-element magma are investigated in this study, focusing on the case when the magma is a group or a hypergroup. It is shown that state machines in any two-element magma can only have up to three states. In particular, the quasi-automata and quasi-multiautomata state machines are described and enumerated.

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On path hypercompositions in graphs and automata

Cited by 10 publications

References 10 publications

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Cyclicity in EL–Hypergroups

State Machines and Hypergroups

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