Development of an automaton based on rigid logic to control the irrigation system

Managing the distribution of water resources for the southern regions of Russia is of great importance in connection with limiting the consumption of fresh water. The use of saline water can lead to soil salinization and negatively affect crop production. The article deals with the problem of constructing a sequential automaton for controlling the system of switching networks when watering plants on the example of the sanatorium “Rus” in the city of Anapa, Krasnodar Territory. The Mediterranean zone, where the city of Anapa is located, is characterized by a low level of precipitation, which leads to the need for artificial irrigation of plants. The existing irrigation system using a water tank truck based on the GAZ-53 is physically outdated, which required the development of a modern automated system. The flower alleys, located on the territory of the sanatorium, were structured in a tree-like form. The construction of a control device based on rigid logic is based on the Mealy automaton. A method for constructing a control system for a tree-like water supply network has been developed, which makes it possible to control the main, distribution and supply branches. A block diagram of an irrigation machine has been developed, which has a tree-like branching, which shows control signals and states of transitions. Synthesized logical equations for the control of the water supply system, using a blocking control system with feedback. It is proposed to use the Omron programmable logic controller and CX-One software as software and hardware. The distribution of the address space of the controller is shown. Simulation modeling of the system operation was carried out, which showed the correct logic of control over the work of water pressure supply in water pipelines. Implementation of the developed system will improve the quality of irrigation of plants and minimize the cost of irrigation.

Boundary dynamics for bireversible and for contracting automaton groups

We study the dynamics of the action of an automaton group on the set of infinite words, and more precisely the discontinuous points of the map which associates to a point its set of stabilizers — the singular points. We show that, for any Mealy automaton, the set of singular points has measure zero. Then we focus our attention on several classes of automata. We characterize those contracting automata generating groups without singular points, and apply this characterization to the Basilica group. We prove that potential examples of reversible automata generating infinite groups without singular points are necessarily bireversible. We also provide some conditions for such examples to exist. Finally, we study some dynamical properties of the Schreier graphs in the boundary.

BASIC PRINCIPLES OF BUILDING BLACK-BOX VULNERABILITY SCANNER OF WEB RESOURCE

The article discusses the main provisions for constructing a vulnerability scanner for a web resource based on the «black box» technique. The definitions of the Mealy automaton are introduced, applicable to the web application. An example of the use of the Mealy automaton for constructing transition graphs on the links of a web resource is given. An algorithm for constructing a graph based on sent requests and received answers is proposed. Describe the alleged problems that arise in the scanner. There are proposed ways of solving the problems obtained with the use of additional mechanisms and work algorithms. When the algorithm is running and transitions are added, the new vertex is colored with one of the colors, if a repeated state is detected. As a result, we have a colored graph, which may collapse in the same colors. The user in the browser moving inside the web application performs sequential actions, the scanning technique is as close as possible to the real actions of the average user and provides a top-down view of the content, as well as the probability of clicking on the link. Thus determined group of sequential requests that change the state of the scanner.

A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group

The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, all such examples have been constructed as groups generated by non-reversible automata. Moreover, it was recently shown that 2-state reversible Mealy automata cannot generate infinite Burnside groups. Here we extend this result to connected 3-state reversible Mealy automata, using new original techniques. The results rely on a fine analysis of associated orbit trees and a new characterization of the existence of elements of infinite order.

THE FINITENESS PROBLEM FOR AUTOMATON SEMIGROUPS IS UNDECIDABLE

The finiteness problem for automaton groups and semigroups has been widely studied, several partial positive results are known. However, we prove that, in the most general case, the problem is undecidable. We study the case of automaton semigroups. Given a NW-deterministic Wang tile set, we construct a Mealy automaton, such that the plane admits a valid Wang tiling if and only if the Mealy automaton generates a infinite semigroup. The construction is similar to a construction by Kari for proving that the nilpotency problem for cellular automata is unsolvable. Moreover, Kari proves that the tiling of the plane is undecidable for NW-deterministic Wang tile set. It follows that the finiteness problem for automaton semigroups is undecidable.

ON GENERATION OF WREATH PRODUCTS OF CYCLIC GROUPS BY TWO STATE TIME VARYING MEALY AUTOMATA

We proof that an infinitely iterated wreath product of finite cyclic groups of pairwise coprime orders is generated as a topological group by two elements a and b. The group G = 〈a, b〉 may be represented by a 2-state time-varying Mealy automaton. We derive some properties of G.