Modified product of automata as a better tool for description of real-life systems

From Automata to Multiautomata via Theory of Hypercompositional Structures

“…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 :…”

n-Ary Cartesian Composition of Multiautomata with Internal Link for Autonomous Control of Lane Shifting

“…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.…”

“…Therefore, we include the following definition. For an example explaining the concept (together with calculations) see [21], Example 1. Definition 5 ([21]).…”

“…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.…”

“…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 .…”