A Concrete View of Rule 110 Computation

@inproceedings{Cook2008ACV,
  title={A Concrete View of Rule 110 Computation},
  author={Matthew Cook},
  booktitle={CSP},
  year={2008}
}
Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed to 0s at all positions where the values to the left and right are both 1. Though trivial to define, the behavior exhibited by Rule 110 is surprisingly intricate, and in (Cook, 2004) we showed that it is capable of emulating the activity of a… 

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References

SHOWING 1-10 OF 12 REFERENCES

Universality in Elementary Cellular Automata

The purpose of this paper is to prove that one of the simplest one dimensional cellular automata is computationally universal, implying that many questions concerning its behavior, such as whether a

Universality of Tag Systems with P = 2

The representation of the Turing machine in the present system has a lower degree of exponentiation, which may be of significance in applications, and these systems seem to be of value in establishing unsolvability of combinatorial problems.

A new kind of science

A New Kind of Science, written and published by Stephen Wolfram, is the outcome of the studies he conducted systematically upon cellular automata, a class of computer model which may be visualized as a set of memory locations, each containing one bit.

P-completeness of Cellular Automaton Rule 110

It is shown that the problem of predicting t steps of the 1D cellular automaton Rule 110 is P-complete and the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their previously known simulation time overhead.

Small Weakly Universal Turing Machines

These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right, and are currently the smallest knownWeakly universal Turing machines.

Tag systems and Collatz-like functions

On the time complexity of 2-tag systems and small universal Turing machines

  • D. WoodsT. Neary
  • Computer Science
    2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
  • 2006
We show that 2-tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial

Small Universal Turing Machines

The 2-symbol Turing machine simulating Rul e 110 requires only 7 states

  • (personal communication)
  • 1998

A tag system for the 3x+1 problem

  • (personal c ommunication)
  • 2003