*Article* **State Machines and Hypergroups**

**Gerasimos G. Massouros 1,\* and Christos G. Massouros <sup>2</sup>**


**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.

**Keywords:** hypergroup; magma; state machines; automata

**MSC:** 20N20; 18B20; 68Q70
