Turing-complete | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-01-13

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Turing_completeness


00:02:35 1 Non-mathematical usage
00:03:52 2 Formal definitions
00:06:00 3 History
00:09:40 4 Computability theory
00:12:14 5 Turing oracles
00:13:06 6 Digital physics
00:13:46 7 Examples
00:17:57 7.1 Unintentional Turing completeness
00:18:41 8 Non-Turing-complete languages
00:20:39 8.1 Data languages
00:21:35 9 See also



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SUMMARY
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In computability theory, a system of data-manipulation rules (such as 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. This means that this system is able to recognize or decide other data-manipulation rule sets. This Turing completeness is used as a way to express the power of such data-manipulation rule set. The expression power of these grammars is captured in the Chomsky hierarchy. Virtually all programming languages today are Turing Complete. The concept is named after English mathematician and computer scientist Alan Turing. A classic example is lambda calculus.A closely related concept is that of Turing equivalence –  two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing machine. A universal Turing machine can be used to simulate any Turing machine and by extension the computational aspects of any possible real-world computer.To show that something is Turing complete, it is enough to show that it can be used to simulate some Turing complete system. For example, an imperative language is Turing complete if it has conditional branching (e.g., "if" and "goto" statements, or a "branch if zero" instruction; see one instruction set computer) and the ability to change an arbitrary amount of memory (e.g., the ability to maintain an arbitrary number of data items). Of course, no physical system can have infinite memory; but if the limitation of finite memory is ignored, most programming languages are otherwise Turing complete.