State Machines and Hypergroups

Abstract

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.

Preface to the Special Issue “Algebraic Structures and Graph Theory”

“…Furthermore, they prove that for any positive integer n greater than 1, there exists an infinite quotient hyperfield of characteristic n. A similar result holds for the C-characteristic. The manuscripts [11,12] cover some applications of hypercompositional algebra to automata theory. Massouros et al [11] study the binary state machines with magma of two elements as their environment.…”

“…The manuscripts [11,12] cover some applications of hypercompositional algebra to automata theory. Massouros et al [11] study the binary state machines with magma of two elements as their environment. Another aspect of automata theory is discussed in [12], where the authors propose several conditions for simplifying the verification of the GMAC condition for systems of quasi-multiautomata.…”