Turing completeness

New languages with new features are always being created, so proof of Turing completeness is always a challenge.

Turing completeness is an abstract statement of ability, rather than a prescription of specific language features used to implement that ability.

The need for a structuring convention arises since PostScript is a Turing completeness programming language.

One specific new technical result in the book is a description of the Turing completeness of the Rule 110 cellular automaton.

Turing completeness is significant in that every real-world design for a computing device can be simulated by a universal Turing machine.

Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing completeness system.

Turing completeness can be obtained by using nine membranes together with the operations of endocytosis and exocytosis [21].

Turing completeness of Prolog can be shown by using it to simulate a Turing machine:

Turing Completeness Using Three Mobile Membranes.

However, several concepts developed by computer scientists are essential to understanding the argument, including symbol processing, Turing machines, Turing completeness, and the Turing test.

Per the Turing completeness, a simulation can progress at whatever speed its host computer can manage; it would be constrained by available memory but not by computation rate.

Turing completeness, as just defined above, corresponds only partially to Turing completeness in the sense of computational universality.

Turing completeness is a favorite topic of discussion, since it is not immediately obvious whether or not a language is Turing complete, and it often takes rather large intuitive leaps to come to a solution.

The operational semantics of BCL, apart from eta-reduction (which is not required for Turing completeness), may be very compactly specified by the following rewriting rules for subterms of a given term, parsing from the left:

Leibniz's idea of reasoning through a universal language of symbols and calculations however remarkably foreshadows great 20th century developments in formal systems, such as Turing completeness, where computation was used to define equivalent universal languages (see Turing degree).

The features used to achieve Turing completeness can be quite different; Fortran systems would use loop constructs or possibly even goto statements to achieve repetition; Haskell and Prolog, lacking looping almost entirely, would use recursion.

It was used by Graham to illustrate a comparison of power between programming languages that go beyond Turing completeness, and more specifically, to illustrate the difficulty of comparing a programming language one knows to one that one does not:

However, since the C preprocessor does not have features of some other preprocessors, such as recursive macros, selective expansion according to quoting, string evaluation in conditionals, and Turing completeness, it is very limited in comparison to a more general macro processor such as m4.

Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been proven, although proofs for several similar rules should follow as simple corollaries, for instance Rule 124, where the only directional (asymmetrical) transformation is reversed.

Conversely, all iterative functions and procedures that can be evaluated by a computer (see Turing completeness) can be expressed in terms of recursive functions; iterative control constructs such as while loops and do loops routinely are rewritten in recursive form in functional languages.

Structured programming, canonical structures: Per the Church-Turing thesis any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations Turing completeness requires only four instruction types-conditional GOTO, unconditional GOTO, assignment, HALT.

It was not then realized that Turing completeness was significant; most of the other pioneering modern computing machines were also not Turing complete (e.g. the Atanasoff-Berry Computer, the Bell Labs relay machines (by George Stibitz et al.), or the first designs of Konrad Zuse).