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A Turing machine is a mathematical model of computation describing an abstract machine [1] ... Two-tape simulation of multitape Turing machines.
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, [1] as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible.
It is possible to build a pattern that acts like a finite-state machine connected to two counters. This has the same computational power as a universal Turing machine, so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints; it is Turing complete.
In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine.
Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been directly proven, although proofs for several similar rules follow as simple corollaries (e.g. Rule 124, which is the horizontal reflection of Rule 110). Rule 110 is arguably the simplest known Turing complete system. [2] [5]
The 2-tag system is an efficient simulator of universal Turing machines, in () time. That is, if M {\displaystyle M} is a deterministic single-tape Turing machine that runs in time t {\displaystyle t} , then there is a 2-tag system that simulates it in O ( t 4 ln 2 t ) {\displaystyle O(t^{4}\ln ^{2}t)} time.
Developed by Tomas Rokicki and Andrew Trevorrow. This is the only simulator currently available that can demonstrate von Neumann type self-replication. Wolfram Atlas – An atlas of various types of one-dimensional cellular automata. Conway Life; Cellular automaton FAQ from the newsgroup comp.theory.cell-automata
With regard to what actions the machine actually does, Turing (1936) [2] states the following: "This [example] table (and all succeeding tables of the same kind) is to be understood to mean that for a configuration described in the first two columns the operations in the third column are carried out successively, and the machine then goes over into the m-configuration in the final column."