P-completeness of Cellular Automaton Rule 110

  • Turlough Neary
  • Damien Woods
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


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.


Cellular Automaton Turing Machine Transition Rule Data Word Tape Data 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Turlough Neary
    • 1
  • Damien Woods
    • 2
  1. 1.TASS, Department of Computer ScienceNational University of Ireland MaynoothIreland
  2. 2.Department of Mathematics and Boole Centre for Research in InformaticsUniversity College CorkIreland

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