*Article* **From Automata to Multiautomata via Theory of Hypercompositional Structures**

**Št ˇepán Kˇrehlík 1, Michal Novák 2,\* and Jana Vyroubalová <sup>2</sup>**


**Abstract:** In this paper, we study two important problems related to quasi-multiautomata: the complicated nature of verification of the GMAC condition for systems of quasi-multiautomata, and the fact that the nature of quasi-multiautomata has deviated from the original nature of automata as seen by the theory of formal languages. For the former problem, we include several new conditions that simplify the procedure. For the latter problem, we close this gap by presenting a construction of quasi-multiautomata, which corresponds to deterministic automata of the theory of formal languages and is based on the operation of concatenation.

**Keywords:** automata theory; hypergroups; quasi-automata; quasi-multiautomata; semiautomata

**MSC:** 20N20; 68Q70
