Search results
Results From The WOW.Com Content Network
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).
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 "Total Turing test" [3] variation of the Turing test, proposed by cognitive scientist Stevan Harnad, [110] adds two further requirements to the traditional Turing test. The interrogator can also test the perceptual abilities of the subject (requiring computer vision ) and the subject's ability to manipulate objects (requiring robotics ).
Turing complete set, a related notion from recursion theory; Completeness (knowledge bases), found in knowledge base theory; Complete search algorithm, a search algorithm that is guaranteed to find a solution if there is one; Incomplete database, a compact representation of a set of possible worlds
The success of the Church–Turing thesis prompted variations of the thesis to be proposed. For example, the physical Church–Turing thesis states: "All physically computable functions are Turing-computable." [54]: 101 The Church–Turing thesis says nothing about the efficiency with which one model of computation can simulate another.
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:
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.
If τ 1 and τ 2 are terms, then (τ 1 τ 2) is a term. Nothing is a term if not required to be so by the first two rules. Derivations : A derivation is a finite sequence of terms defined recursively by the following rules (where α and ι are words over the alphabet { S , K , I , (, )} while β, γ and δ are terms):