Universal groups of cellular automata

نویسندگان

چکیده

We prove that the group of reversible cellular automata (RCA), on any alphabet $A$, contains a subgroup generated by three involutions which an isomorphic copy every finitely RCA $B$. This result follows from

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Intrinsically Universal Cellular Automata

This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with respect to Turing and circuit universality, we discuss construction methods for small intrinsically universal cellular automata before discussing techniques for ...

متن کامل

About Strongly Universal Cellular Automata

In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving rise to strongly universal cellular automata with 10 states.

متن کامل

Universal Cellular Automata in the Hyperbolic Spaces

This paper introduces several cellular automata in hyperbolic spaces which are able to simulate any computational device, as they are universal. We sketchily present five universal cellular automata, four of them on two grids of the hyperbolic plane and one in a grid of the hyperbolic 3D space. Key–Words: Theory of Computation, Cellular Automata, universality, hyperbolic geometry.

متن کامل

Quasi-Uniform Computation-Universal Cellular Automata

Cellular automata (CA) are dynamical systems in which space and time are discrete , where each cell obeys the same rule and has a nite number of states. In this paper we study non-uniform CA, i.e. with non-uniform local interaction rules. Our focal point is the issue of universal computation, which has been proven for uniform automata using complicated designs embedded in cellular space. The co...

متن کامل

Intrinsically universal one-dimensional quantum cellular automata

We give a one-dimensional quantum cellular automata (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will then correspond to one step of the simulated QCA. The simulation preserves the topology in ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Colloquium Mathematicum

سال: 2022

ISSN: ['0010-1354', '1730-6302']

DOI: https://doi.org/10.4064/cm8368-9-2021