![]() ) (Computational) universality A system is called universal with respect to a class of systems if it can compute every function computable by systems in that class (or can simulate each of those systems). (All known physically-implementable Turing-complete systems are Turing-equivalent, which adds support to the Church–Turing thesis. Alternatively, a Turing-equivalent system is one that can simulate, and be simulated by, a universal Turing machine. Turing equivalence A Turing-complete system is called Turing-equivalent if every function it can compute is also Turing-computable i.e., it computes precisely the same class of functions as do Turing machines. Alternatively, such a system is one that can simulate a universal Turing machine. Turing completeness A computational system that can compute every Turing- computable function is called Turing-complete (or Turing-powerful). ![]() In computability theory, several closely related terms are used to describe the computational power of a computational system (such as an abstract machine or programming language): In contrast, a universal computer is defined as a device with a Turing-complete instruction set, infinite memory, and infinite available time. However, real computers have limited physical resources, so they are only linear bounded automaton complete. Real computers constructed so far can be functionally analyzed like a single-tape Turing machine (the "tape" corresponding to their memory) thus the associated mathematics can apply by abstracting their operation far enough. In real life, this leads to the practical concepts of computing virtualization and emulation. In colloquial usage, the terms "Turing-complete" and "Turing-equivalent" are used to mean that any real-world general-purpose computer or computer language can approximately simulate the computational aspects of any other real-world general-purpose computer or computer language. No physical system can have infinite memory, but if the limitation of finite memory is ignored, most programming languages are otherwise Turing-complete. To show that something is Turing-complete, it is enough to show that it can be used to simulate some Turing-complete system. A universal Turing machine can be used to simulate any Turing machine and by extension the computational aspects of any possible real-world computer. 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. Virtually all programming languages today are Turing-complete.Ī 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. Turing completeness is used as a way to express the power of such a data-manipulation rule set. ![]() This means that this system is able to recognize or decide other data-manipulation rule sets. ![]() 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 (devised by English mathematician and computer scientist Alan Turing). For the usage of this term in the theory of relative computability by oracle machines, see Turing reduction. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |