Algebraic properties of linear cellular automata
نویسندگان
چکیده
منابع مشابه
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...
متن کاملAlgebraic Characterizations of Unitary Linear Quantum Cellular Automata
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the quantum cellular automata’s computational power. The configurations we consider have finite but unbounded size.
متن کاملAlgebraic Properties of the Block Transformation on Cellular Automata
By grouping several sites together into one a cellular automaton can be transformed into another with more states and a smaller neighbor hood if the neighborhood has just two sites we can think of the resulting CA rule as a binary operation We show that if the blocked rule satis es an identity which holds for a broad class of algebras then the underly ing rule must have essentially the same str...
متن کاملBounds for One-dimensional Cellular Automata: A Linear Algebraic Approach
In [CK05], E. Czeizler and J. Kari used a linear algebraic tool to obtain good upper bounds for the length of the inverse neighbourhood of reversible one-dimensional cellular automata (CA). Recently, a linear algebraic approach similar to the one used by J. Kari in [Kar03], lead to better upper bounds for the length of the shortest unbalanced words, shortest orphans and shortest diamonds of non...
متن کاملCellular 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 ...
متن کاملذخیره 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: Linear Algebra and its Applications
سال: 1991
ISSN: 0024-3795
DOI: 10.1016/0024-3795(91)90116-e