CELLULAR AUTOMATA OVER ALGEBRAIC STRUCTURES

Decision Problems for Finite Automata over Infinite Algebraic Structures

Cellular Automata as Algebraic Systems

Infinite cellular automata have been studied mostly using empirical and sta tistical techniques, with some combinatorial analysis. Here we show how concepts of universal algebra such as subdirect decomposition and chains of varieties can be applied to their study. Cellular automata with ultimately periodic behavior are shown to correspond to varieties of groupoids. Relat ionships between these ...

Algebraic Properties of Cellular Automata

Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are...

Designing Cellular Automata Structures using Quantum-dot Cellular Automata

Quantum-dot Cellular Automata (QCA) is a promising, emerging nanotechnology based on single electron effects in quantum dots and molecules. While many logic implementations based on QCA devices have been proposed in literature [6, 7, 8], the inherent cellular structure of QCA cells make it a natural candidate for Cellular Automata (CA) implementation. CA offers regularity and modularity to the ...

SOME HYPER K-ALGEBRAIC STRUCTURES INDUCED BY MAX-MIN GENERAL FUZZY AUTOMATA

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...