A design of real-time non-regular sequence generation algorithms and their implementations on cellular automata with 1-bit inter-cell communications

Abstract

We introduce a special new class of cellular automata(CA) whose inter-cell communication is restricted to 1-bit. Several design examples for 1-bit inter-cell communication cellular algorithms are given. It is shown that infinite non-regular sequences such as {2^n | n = 1, 2, 3,..}, {n^2 |n = 1, 2, 3,..} and Fibonacci sequences can be generated in real-time by cellular automata with 1-bit inter-cell communications. In addition, twice real-time prime generation algorithm is also given.