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

Abstract

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.

From Automata to Multiautomata via Theory of Hypercompositional Structures

“…Currently, the combinations of algebraic multiautomata into higher entities, using various rules suggested by Dörfler [20,26], are studied-see, e.g., [27]. Such combinations seem to be suitable tools for modeling various real-life systems-see, e.g., [16,21,28]-or are even tools to control such systems [22]. However, two main problems appeared in this respect:…”

“…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.…”

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

“…Furthermore, for clarification and evolution of terminology, see [8]. For results obtained by means of quasi-multiautomata, see, e.g., [5][6][7][8]27]. In this section, R n [x] means, as usually, the ring of polynomials of degree at most n.…”

State Machines and Hypergroups

“…There followed more papers by the same author and Ch. Massouros, e.g., [13][14][15][16][17][18][19][20][21], as well as other researchers such as J. Chvalina [22][23][24][25][26][27][28], L. Chvalinová [22], Š. Hošková-Mayerová [24,25], M. Novák [26][27][28][29][30][31][32], S. Křehlík [26,27,[29][30][31]33], M.M. Zahedi [34], M. Ghorani [34,35], D. Heidari and S. Doostali [36], R.A. Borzooei et al [37].…”