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Real-Time Generation of Primes by a 1-Bit-Communication Cellular Automaton

Umeo H., Kamikawa N.

Fundamenta Informaticae

2003

Vol. 58, nr 3,4

421--435

It is shown that an infinite prime sequence can be generated in real-time by a cellular automaton having 1-bit inter-cell communications (CA1-bit). The algorithm presented is based on the classical sieve of Eratosthenes, and its implementation will be made on а СА1-bitusing 34 internal states and 71 transition rules.

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

Umeo H., Kamikawa N.

Fundamenta Informaticae

2002

Vol. 52, nr 1-3

255-275

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.