Scale-invariant cellular automata and self-similar Petri nets

Details Scale-invariant cellular automata and self-similar Petri nets Scale-invariant cellular automata and self-similar Petri nets

2006-06-01

arxiv.org/abs/nlin/0606007v3

The European Physical Journal B 69, 297-311 (2009)

Nonlinear Sciences

Cellular Automata and Lattice Gases

35 pages, 5 figures

Scientific paper

10.1140/epjb/e2009-00147-x

Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.

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