n-ary Cartesian composition of automata

Elements of Hyperstructure Theory in UWSN Design and Data Aggregation

“…In fact, we could speak of semiautomata or deterministic finite automata (the below mentioned paper Chvalina and Chvalinová [25] uses a general term automaton; however, notice that [25], p. 107, plain text, defines automaton in the way of Definition 4, which is a definition adopted by the authors of [25] in later years). For an overall discussion of the concepts and the reasons for our choice of the name see Novák et al [30]. For some further reading and applications see also Hošková et al [31][32][33].…”

“…Further on, we will make use of the above mentioned concepts to model the process of data aggregation. Notice that in Novák et al [30], Cartesian composition of automata resulting in a quasi-multiautomaton is used to describe a task from collective robotics. Moreover, in Chvalina et al [18], the issue of state sets and input sets having the form of vectors and matrices (of both numbers and special classes of functions) is discussed in the context of quasi-multiautomata.…”

The Symmetry of Lower and Upper Approximations, Determined by a Cyclic Hypergroup, Applicable in Control Theory

“…The above example makes use of a single sensor scan. However, we can process these scans into a whole simple mapping algorithm described in [12,26] or improved algorithm via particle filter described in [27]. Figure 6.…”

“…With the help of matrix calculus, which we believe is a suitable tool, we construct cyclic hypergroups and their invertible subhypergroups. Notice that matrix calculus linked to the theory of algebraic hypercompositional structures has been used as a suitable tool in various contexts such as [12][13][14]. Since the notion of hypercompositional cyclicity has a rather complicated evolution, we recommend the reader to study [15], which gives a complex discussion of the topic, and [16] which is the source of our definition.…”

Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

“…In several papers, published mainly as conference proceedings such as [2][3][4], the existing theory was extended by the use of hypercompositional structures in place of the usual algebraic structures. The use of hypercompositional generalizations has been tested in the automata theory, where it has brought several interesting results; see, e.g., [5][6][7][8]. Naturally, this approach is not the only possible one.…”