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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 in...
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... in the case of the Cartesian composition, the situation is different. Since in the definition of the Cartesian composition the state set is created as the Cartesian product of the state set of the respective quasi-multiautomata, it is obvious from Figure 7 that the necessary condition tn(r, t) = 1 is not satisfied in the resulting quasi-multiautomaton, as there is no direct path from state (s 0 , t 0 ) to state (s 1 , t 1 ) because the respective input elements can affect one component only. For a deeper insight into this issue, we refer the reader to Example 1 in [17], the proof of Theorem 2 in [22], or Example 4 in [16], where the GMAC condition is not satisfied anywhere and we consider modified GMAC conditions, called E-GMAC. ...
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... 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. ...
... 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. Furthermore, using the concatenation, they construct quasi-multiautomata corresponding to the deterministic automata of the theory of formal languages. ...
Connections between algebraic structure theory and graph theory have been established in order to solve open problems in one theory with the help of the tools existing in the other, emphasizing the remarkable properties of one theory with techniques involving the second [...]
... The methods by which the input is transferred to the output necessarily depend on the specific type of automaton. Although there is a close connection between automata from the theory of formal languages and theory of algebraic automata, the requirements for the transition function are different, for detail see Novák et al. (2020) and Křehlík et al. (2022). In the theory of formal languages, emphasis is placed on the concatenation of input symbols and the acceptance of the language, i.e., for all strings that lead to the final state, see Massouros (1994a), Jing et al. (2015) and Massouros and Massouros (2020). ...
... The formal definition is introduced in the following section. Details about these terms can be found in Křehlík et al. (2022) and Novák et al. (2020). ...
In this work, we follow the construction of an n -ary system of Cartesian composition of multiautomata with internal links, where we define the internal links to the homogeneous and heterogeneous products of multi-automata. While the introduction of an internal link is rectilinear in the Cartesian composition, it requires a new approach in product construction for the other two automata products. In this way, it is possible to focus on multiple options for creating these systems. More specifically, we combine automata and multi-automata with binding according to the basic definitions given by Dörfler. This approach shows new connections to cellular automata, which allow for the modeling of phenomena in many areas. At the end of the work, we discuss the advantages of these individual schemes for quasi-multiautomata connections.
... The free monoid of the words generated by an alphabet Σ can be endowed with the B-hypergroup structure, and so become a join hyperringoid [21,[72][73][74], which is named linguistic hyperringoid [14,21,73,74]. If the B-hypergroup is fortified with a strong identity [31], which is necessary for the theory of formal languages and automata [14,21], then the join hyperring comes into being [72][73][74]. 7 H is the two-element total hypergroup. ...
... The free monoid of the words generated by an alphabet Σ can be endowed with the B-hypergroup structure, and so become a join hyperringoid [21,[72][73][74], which is named linguistic hyperringoid [14,21,73,74]. If the B-hypergroup is fortified with a strong identity [31], which is necessary for the theory of formal languages and automata [14,21], then the join hyperring comes into being [72][73][74]. H 7 is the two-element total hypergroup. ...
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.
