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...

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...

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...

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...

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

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

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

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

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

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

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...

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

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...

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

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

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

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...

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

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

exists a Turing machine that decides the formal language. In theoretical computer science, such always-halting Turing machines are called total Turing machines...

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...

{\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...

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...

sense that they are all encodable into each other, supports the Church-Turing thesis. Another shared feature is more rarely commented on: they all are...

especially those in accordance with effective methods of the Church-Turing thesis. The thesis states that a mathematical method is effective if it could...

and field-programmable gate array-based hardware emulators. The Church–Turing thesis implies that theoretically, any operating environment can be emulated...

of the environment. Such a game-playing machine generalizes the Church–Turing thesis to the interactive level. The classical concept of truth turns out...