Complexity of Langton's Ant

Nonlinear Sciences – Cellular Automata and Lattice Gases

Scientific paper

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8 pages, 9 figures. Complements at http://www.dim.uchile.cl/~agajardo/langton

Scientific paper

The virtual ant introduced by C. Langton has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one dimensional cellular automata and Turing machines, the universality of the ant and the undecidability of some problems associated to it.

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