A Basis Set of Operators for Space-Time Computations

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Jacob Beal
Proceedings of the 2010 Fourth IEEE International Conference on Self-Adaptive and Self-Organizing Systems Workshop (SASOW 2010), pages 91-97
IEEE Computer Society, Washington, DC, USA

Although many different models of spatial computation have been proposed, no unifying theory of computation over continuous space-time has yet been developed. Lack of such a theory has made it difficult to compare spatial computing models and impossible to determine their completeness. This paper takes a step toward the goal of a unifying model by identifying a mathematical basis set of operators from which any finitely-approximable causal computation can be constructed. The utility of this basis set of operators is then further demonstrated by using it to analyze the universality of the Proto spatial computing programming language.