P-completeness of cellular automaton rule 110

Authors:
Turlough Neary;Damien Woods
Affiliations:
TASS, Department of Computer Science, National University of Ireland Maynooth, Ireland;Department of Mathematics and Boole Centre for Research in Informatics, University College Cork, Ireland
Venue:
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Year:
2006

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Abstract

We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is P-complete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their previously known simulation time overhead.