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

One from classical constructions of algebraic binary hyperstructures (semihypergroups and hypergroups) from ordered algebraic systems is based on a certain Lemma on principal ends generated by products of pairs of elements – shortly termed as Ends-Lemma. First version of this auxiliary lemma was obtained in the monography [3]. The mentioned lemma is applied not only in case of hyperstructures c...

This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

Using the derived algebraic formalism of Lurie we describe a framework for coalgebraic structures which are neither necessarily commutative nor cocommutative. We show that Thom spectra and homotopical descent data are both natural examples of this kind of structure.