A Design of Real-Time Non-Regular Sequence Generation Algorithms and Their Implementations on Cellular Automata with 1-Bit Inter-Cell Communications

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 {2n | n = 1, 2, 3,..}, { n2 | 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.