“…Definition 11. [21] Let A 1 = (I, S, δ), A 2 = (I, R, τ), and B = (J, T, σ) be quasi-automata. By the homogeneous product A 1 × A 2 , we mean the quasi-automaton (I, S × R, δ × τ), where δ × τ :…”
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.
“…Definition 11. [21] Let A 1 = (I, S, δ), A 2 = (I, R, τ), and B = (J, T, σ) be quasi-automata. By the homogeneous product A 1 × A 2 , we mean the quasi-automaton (I, S × R, δ × τ), where δ × τ :…”
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.
“…When modelling the process of data aggregation from underwater wireless sensor networks, Křehlík and Novák [21] suggested that using an internal link between respective automata in their cartesian composition describes the real-life context better because the internal link influences not only the given individual automaton but to a certain extent the whole system. In this paper we make use of [21]. Therefore, we include the following definition.…”
Section: Definition 4 ([13]mentioning
confidence: 99%
“…Therefore, we include the following definition. For an example explaining the concept (together with calculations) see [21], Example 1. Definition 5 ([21]).…”
Section: Definition 4 ([13]mentioning
confidence: 99%
“…In [9,13,19,20] we presented some real-life applications. In this section, we introduce an extension of ideas first included in [21] regarding internal links in the cartesian composition of quasi-multiautomata. We discuss systems in which there is a whole set of internal links.…”
Section: New Theoretical Modelmentioning
confidence: 99%
“…where 2 M ı n,m is a suitable matrix which enables us to obtain a state matrix with entries given in Figure 7 for the state of MA 2 . After we apply the input obtained by the internal link ϕ 32 in Equation (21) with the help of transition function δ 2 , we get a new state depicted in Figure 7 for e-quasi-multiautomaton MA 2 .…”
In this paper, which is based on a real-life motivation, we present an algebraic theory of automata and multi-automata. We combine these (multi-)automata using the products introduced by W. Dörfler, where we work with the cartesian composition and we define the internal links among multiautomata by means of the internal links’ matrix. We used the obtained product of n-ary multi-automata as a system that models and controls certain traffic situations (lane shifting) for autonomous vehicles.
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