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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]
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine [1] [2] (devised by English mathematician and computer scientist Alan Turing).
For example, the index set FIN of the class of all finite sets is on the level Σ 2, the index set REC of the class of all recursive sets is on the level Σ 3, the index set COFIN of all cofinite sets is also on the level Σ 3 and the index set COMP of the class of all Turing-complete sets Σ 4.
The counter machine models go by a number of different names that may help to distinguish them by their peculiarities. In the following the instruction "JZDEC ( r )" is a compound instruction that tests to see if a register r is empty; if so then jump to instruction I z, else if not then DECrement the contents of r:
Arithmetic-based Turing-complete machines use an arithmetic operation and a conditional jump. Like the two previous universal computers, this class is also Turing-complete. The instruction operates on integers which may also be addresses in memory. Currently there are several known OISCs of this class, based on different arithmetic operations:
A Turing degree is an equivalence class of the relation ≡ T. The notation [X] denotes the equivalence class containing a set X. The entire collection of Turing degrees is denoted . The Turing degrees have a partial order ≤ defined so that [X] ≤ [Y] if and only if X ≤ T Y. There is a unique Turing degree containing all the computable ...
Ultrakill is an upcoming first-person shooter video game developed by Arsi "Hakita" Patala and published by New Blood Interactive. It was released on Steam through early access for Microsoft Windows on 3 September 2020. [ 1 ]
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.