A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin

Self-repair ability of evolved self-assembling systems in cellular automata

Self-repairing systems are those that are able to reconfigure themselves following disruptions to bring them back into a defined normal state. In this paper we explore the self-repair ability of some cellular automata-like systems, which differ from classical cellular automata by the introduction of a local diffusion process inspired by chemical signalling processes in biological development. The update rules in these systems are evolved using genetic programming to self-assemble towards a target pattern. In particular, we demonstrate that once the update rules have been evolved for self-assembly, many of those update rules also provide a self-repair ability without any additional evolutionary process aimed specifically at self-repair

Measurements, Models, Systems and Design

531 s.

Quantum Games and Programmable Quantum Systems

Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over the classical approach. Game theory, the study of decision making in conflict situation has already been extended to the quantum domain. We would like to review the latest development in quantum game theory that is relevant to information processing. We will begin by illustrating the general idea of a quantum game and methods of gaining an advantage over "classical opponent". Then we review the most important game theoretical aspects of quantum information processing. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is explained.

Синтез совмещенного автомата в базисе ASIC

Предложен метод синтеза схемы совмещенного автомата в базисе заказных интегральных схем. Метод основан на расширении матрицы, генерирующей термы систем функций возбуждения памяти и выходных функций. Дополнительная часть матрицы генерирует термы для выходных функций автомата Мура и позволяет уменьшить площадь кристалла по сравнению с площадью двухуровневой схемы автомата. Приведены результаты исследований и пример синтеза схемы автомата.Мета роботи. Показати, як розділення матриць схеми автомата дозволяє зменшити результуючу площу схеми. При цьому оцінки витрат апаратури для тривіальної структури автомата і запропонованого підходу визначаються в умовних одиницях площі. Результати. Запропоновано метод синтезу автомата з розширенням матриці термів. На прикладі показано, як виконувати кроки запропонованого методу синтезу. Для збільшення ефективності методу запропоновано використовувати спеціальне кодування станів, яке мінімізує число термів у системах булевських функцій для виходів автомата Мура. Дослідження, проведені на стандартних автоматах, показали, що запропонований метод призводить до зменшення площі ASIC від 10 % до 26 %. При цьому виграш зростає за мірою зростання складності автомата.The purpose of the article is to show that the division of circuit matrices allows reducing the resulting matrix area. The hardware amount is estimated for both trivial automaton structure and for the proposed approach. They are determined in conventional units of area. Results. The method is proposed based on the expansion of the matrix of terms. Using an example, it is shown how to execute the steps of the proposed method. To increase the method efficiency, it is proposed to use a special state assignment that minimizes the number of terms in the systems of Boolean functions of outputs with Moore type. The conducted investigations show that the proposed method allows for reducing the resulting ASIC area from 10% to 26%. The gain increases with the growth of the automaton complexity

Sequential Relational Decomposition

The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple and natural formalization of sequential decomposition, in which a task is decomposed into two sequential sub-tasks, with the first sub-task to be executed before the second sub-task is executed. These tasks are specified by means of input/output relations. We define and study decomposition problems, which is to decide whether a given specification can be sequentially decomposed. Our main result is that decomposition itself is a difficult computational problem. More specifically, we study decomposition problems in three settings: where the input task is specified explicitly, by means of Boolean circuits, and by means of automatic relations. We show that in the first setting decomposition is NP-complete, in the second setting it is NEXPTIME-complete, and in the third setting there is evidence to suggest that it is undecidable. Our results indicate that the intuitive idea of decomposition as a system-design approach requires further investigation. In particular, we show that adding a human to the loop by asking for a decomposition hint lowers the complexity of decomposition problems considerably

Identification of the neighborhood and CA rules from spatio-temporal CA patterns

Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually produces a CA rule table without providing a clear understanding of the structure of the neighborhood or the CA rule. In this paper, a new identification method based on using a modified orthogonal least squares or CA-OLS algorithm to detect the neighborhood structure and the underlying polynomial form of the CA rules is proposed. The Quine-McCluskey method is then applied to extract minimum Boolean expressions from the polynomials. Spatio-temporal patterns produced by the evolution of 1D, 2D, and higher dimensional binary CAs are used to illustrate the new algorithm, and simulation results show that the CA-OLS algorithm can quickly select both the correct neighborhood structure and the corresponding rule