the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture...

The history of the Church–Turing thesis ("thesis") involves the history of the development of the study of the nature of functions whose values are effectively...

the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem ("decision problem"), the Frege–Church ontology, and the Church–Rosser...

introduced by Alonzo Church. Church's work intertwined with Turing's to form the basis for the Church–Turing thesis. This thesis states that Turing machines, lambda...

computed by a Turing machine. Hypercomputers compute functions that a Turing machine cannot and which are, hence, not computable in the Church–Turing sense....

known physically-implementable Turing-complete systems are Turing-equivalent, which adds support to the Church–Turing thesis.[citation needed]) (Computational)...

Copeland, B. Jack. "The Church-Turing Thesis". Stanford Encyclopedia of Philosophy. Hodges, Andrew. "Did Church and Turing have a thesis about machines?". Copeland...

true. Turing and Church independently showed in the 1930s that this set of natural numbers is not computable. According to the Church–Turing thesis, there...

of the physical Church–Turing thesis. If the physical Church–Turing thesis holds, and all physically computable functions are Turing-computable, then...

problem considered in Turing's 1936 paper ("does a Turing machine starting from a blank tape ever print a given symbol?"). However, Turing equivalence is rather...

and quantum physics, the Church–Turing–Deutsch principle (CTD principle) is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch...

functions under Church encoding. The Church–Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding.[dubious...

and the Church–Turing Thesis (the hypothesis of "every"). The notion of separating out Church's and Turing's theses from the "Church–Turing thesis" appears...

and some are not. According to the Church–Turing thesis, any effectively calculable function is calculable by a Turing machine, and thus a set S is computably...

argues that super-recursive algorithms can be used to disprove the Church–Turing thesis. This point of view has been criticized within the mathematical community...

Description was given by Turing Award winner Stephen Cook. Aside from a Turing machine, other equivalent (see Church–Turing thesis) models of computation...

functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely...

Alan Turing Year The Annotated Turing Church–Turing thesis Church–Turing–Deutsch principle Good–Turing frequency estimation Object-Oriented Turing (programming...

algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father...

computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the...

is equivalent, in computability terms, to Turing machines, thereby proving the physical Church–Turing thesis for the class of systems modelled by the GPAC...

combinations. Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. Its namesake,...

implications of quantum computing for the modern Church-Turing thesis. In short the modern Church-Turing thesis states that any computational model can be simulated...

computable by a Turing machine (or equivalently, by those expressible in the lambda calculus). This assumption is now known as the Church–Turing thesis. The origin...

{\displaystyle B\leq _{T}A.} The equivalence classes of Turing equivalent sets are called Turing degrees. The Turing degree of a set X {\displaystyle X} is written...

enough memory and time. Turing writes, "all digital computers are in a sense equivalent." The widely accepted Church–Turing thesis holds that any function...

Alonzo Church, Rózsa Péter, Alan Turing, Stephen Kleene, and Emil Post. The fundamental results the researchers obtained established Turing computability...

natural numbers. This would, however, be in contradiction with the Church–Turing thesis. Some have argued this poses a problem for intuitionism, since the...

all total functions are computable functions. The similarly named Church–Turing thesis states that every effectively calculable function is a computable...

Turing's proof is a proof by Alan Turing, first published in November 1936 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem"...