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Štěpán Křehlík and Michal Novák

Abstract

In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures.

Open access

Jan Chvalina, Štěpán Kŕehlík and Michal Novák

Abstract

When we assume that the input-set of an automaton without output is a semihypergroup instead of a monoid, we talk about quasi-multiautomata. Even though cartesian composition of quasi-automata is a commonly used concept, the cartesian composition of quasi-multiautomata has not been successfully constructed yet. In our paper we show that the straightforward transfer of the deffinition into the multivariate context fails. We suggest two possible solutions of this problem.