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Complexity of Langton's ant

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2002Embargo end date: 01 Jan 2003 English Publisher:Elsevier BVJournal:Discrete Applied Mathematics, volume 117, pages 41-50 (issn: 0166-218X, Copyright policy )
Authors: Andrés Moreira; Eric Goles; Anahí Gajardo;

doi: 10.1016/s0166-218x(00)00334-6 , 10.48550/arxiv.nlin/0306022

arXiv: http://arxiv.org/abs/nlin/0306022

Complexity of Langton's ant

Abstract

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.

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

Related Organizations
Keywords

Cellular automata (computational aspects), P-hardness, Virtual ant, Analysis of algorithms and problem complexity, Applied Mathematics, Cellular Automata and Lattice Gases (nlin.CG), FOS: Physical sciences, Complexity, Neural networks for/in biological studies, artificial life and related topics, Universality, Artificial life, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), Discrete Mathematics and Combinatorics, Nonlinear Sciences - Cellular Automata and Lattice Gases

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
46
Top 10%
Top 10%
Average
Green
hybrid