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This project began, generally, in the realm of fungible computing. How do we create an computational automaton that can functionally reproduce and adapt, at run time, according to changing needs? For my project, I am interested in fault tolerance in self reproducing CAs. The primary questions that I would like to address concern scaling - how much fault tolerance is needed, how it can be implemented, and what happens when massively scaled(?). I tentatively propose the simulation and possible physical construction of a CA that performs simple arithmetic operations, and is capable of adopting additions as well as being tolerant to random deletions of elements.

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Von Neumann and his successors (Burks, Thatcher, Lee, Codd, Banks, etc.) developed universal computing automata that is, self reproducing automata capable of simulating a universal Turing machine; unfortunately, the complexity of these automata is such that no physical implementation has yet been [accomplished], and only partial simulations have been realized (Mange et al 1997). Langton and his successors (Byl, Reggia et al.) developed self reproducing automata which are much simpler and which have been simulated in their entirety; these machines, however, lack any computing ability and are capable exclusively of self reproduction (Mange et al 1007).

References

Castro-Leon & Munter (2005) Grid Computing Looking Forward. Intel Solution Services White Paper. Mange, Madon, Stauffer, & Tempesti (1997) Von Neumann revisited: A Turing machine with self repair and self reproduction properties. Robotics and Autonomous Systems 22, 35-38. Tempesti (1995) A New Self Reproducing Cellular Automaton Capable of Construction and Computation. Advances in Artificial Life. AI 929, Springer, Berlin. Bacon, Kempe, DiVincenzo, Lidar, & Whaley (2001) Encoded Universality in Physical Implementations of a Quantum Computer. arXiv:quant-ph/0102140v2. Morita & Imai (1996) A Simple Self Reproducing Cellular Automaton with Shape Encoding Machanism. Artifical Life V. May 16-18. Nara, Japan. Murata, Kurokawa, & Kokaji (1994) Self Assembling Machine. IEEE 1050-4729/94. Pererier, Sipper, & Zahnd (1996) Toward a viable, self reproducing universal computer. Physica D 97, 355-352. Toffoli (2004) Action, or the fungibility of computation. Feynman and Computation (Anthony Hey, ed.), Perseus, 349-392. Wolfram (1983) Statistical mechanics of cellular automata. Reviews of Modern Physics. Vol. 55, No.3, 601-644.

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