Universal computer: Difference between revisions
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In 1982, [[John Conway]] proved in ''[[Winning Ways]]'' that the [[Game of Life]] has a (finite) universal computer, as well as a universal constructor. Proving the universality of a cellular automaton with simple rules was in fact Conway's aim in Life right from the start. The universal computer uses [[glider]] logic and a [[sliding block memory]], and the proof of its existence is also outlined in [[The Recursive Universe]]. | In 1982, [[John Conway]] proved in ''[[Winning Ways]]'' that the [[Game of Life]] has a (finite) universal computer, as well as a universal constructor. Proving the universality of a cellular automaton with simple rules was in fact Conway's aim in Life right from the start. The universal computer uses [[glider]] logic and a [[sliding block memory]], and the proof of its existence is also outlined in [[The Recursive Universe]]. | ||
In 2000, Paul Rendell constructed a direct implementation of a Turing | In April 2000, [[Paul Rendell]] constructed a direct implementation of a [[Turing machine]].<ref>{{cite web|url=http://rendell-attic.org/gol/tm.htm|title=A Turing Machine in Conway's Game of Life|author=Paul Rendell|date=April 2, 2000}}</ref> This computer is infinite, as it requires an infinite length of tape for the Turing Machine. | ||
In 2002, using [[Dean Hickerson]]'s [[sliding block memory]], [[Paul Chapman]] constructed an implementation of a Minsky Register Machine (a machine of the same capability as a Turing Machine), which he extended to a Universal Register Machine, a finite universal computer.<ref>{{cite web|url=http://www.igblan.free-online.co.uk/igblan/ca/|title=Life Universal Computer|author=Paul Chapman|date=November 11, 2002}}</ref> | In 2002, using [[Dean Hickerson]]'s [[sliding block memory]], [[Paul Chapman]] constructed an implementation of a Minsky Register Machine (a machine of the same capability as a Turing Machine), which he extended to a Universal Register Machine, a finite universal computer.<ref>{{cite web|url=http://www.igblan.free-online.co.uk/igblan/ca/|title=Life Universal Computer|author=Paul Chapman|date=November 11, 2002}}</ref> | ||
Revision as of 14:00, 8 June 2009
A universal computer in a cellular automaton is a system that can compute anything that a Turing machine can compute. A cellular automaton in which such a system exists is called universal. A universal computer may be either infinite or finite, but when combined with a universal constructor, it is assumed to be finite.
Universal computers in Life
In 1982, John Conway proved in Winning Ways that the Game of Life has a (finite) universal computer, as well as a universal constructor. Proving the universality of a cellular automaton with simple rules was in fact Conway's aim in Life right from the start. The universal computer uses glider logic and a sliding block memory, and the proof of its existence is also outlined in The Recursive Universe.
In April 2000, Paul Rendell constructed a direct implementation of a Turing machine.[1] This computer is infinite, as it requires an infinite length of tape for the Turing Machine.
In 2002, using Dean Hickerson's sliding block memory, Paul Chapman constructed an implementation of a Minsky Register Machine (a machine of the same capability as a Turing Machine), which he extended to a Universal Register Machine, a finite universal computer.[2]
Universal computers in other cellular automata
David Eppstein and Dean Hickerson proved that 236/35 has a universal computer and universal constructor, using the same method of proof that Conway used to prove that Life is universal.[3]
References
- ↑ Paul Rendell (April 2, 2000). "A Turing Machine in Conway's Game of Life".
- ↑ Paul Chapman (November 11, 2002). "Life Universal Computer".
- ↑ D. Eppstein. "B35/S236".
External Links
- Universal computer at the Life Lexicon