In simple terms, the Church – Turing thesis states that a function is algorithmically computable if and only if it is computable by a Turing machine.

Informally the Church – Turing thesis states that if some method ( algorithm ) exists to carry out a calculation, then the same calculation can also be carried out by a Turing machine ( as well as by a recursively definable function, and by a λ-function ).

While H. Floris Cohen states that most scholars reject crude articulations of the conflict thesis, such as Andrew D. White's, he also states that milder versions of this thesis still hold some sway.

The Church – Turing thesis states that this is a law of mathematics — that a universal Turing machine can, in principle, perform any calculation that any other programmable computer can.

* Forced population transfers in early Ottoman imperial strategy, a comparative thesis that treats the subject in some detail, and includes a general evaluation of the use of population transfers by states in the pre-modern period

Wittgenstein's famous thesis states that meaning is determined by use.

As with Immanuel Velikovsky's earlier Worlds in Collision thesis, Sitchin states that he has found evidence of ancient human knowledge of rogue celestial motions in a variety of mythological accounts.

Nowadays these are often considered as a single hypothesis, the Church – Turing thesis, which states that any function that is computable by an algorithm is a computable function.

The Church – Turing thesis states that any function that is algorithmically computable can be computed by a Turing machine.

For his senior thesis, he investigated the oxidation states of manganese.

This provides an interesting twist on Wallerstein's neo-Marxist interpretation of the international order which faults differences in power relations between ' core ' and ' periphery ' states as the chief cause for economic and political inequality ( However, the Singer-Prebisch thesis also works with different bargaining positions of labour in developed and developing countries ).

In 1988, the group's national committee moved from its original position that the Stalinist states were " deformed or degenerated workers states ", and opened a discussion on the thesis that they were some ' new exploiting society '.

Another popular explanation for the Italian Renaissance is the thesis, first advanced by historian Hans Baron, that states that the primary impetus of the early Renaissance was the long-running series of wars between Florence and Milan.

The staples thesis states that exportation of raw materials can trigger sustainable economic growth-while its critics argue that reliance on commodity export can constitute a development trap.

" Ehrlich further states that he stands behind the central thesis of the book, and that its message is as apt today as it was in 1968.

Since 2006, in some federal states of Germany, there have been new restrictions by the federal laws regarding the degree of the Ph. D. thesis which allow only excellent candidates to enter the habilitation process.

Dunn states that despite Wells ' arguments, the theories of the non-existence of Jesus are a " thoroughly dead thesis ".

The supporters of the Open Letter read this to suggest there would be " centuries of deformed workers states ", and this phrase is often mistaken attributed to Pablo or to his formulation of what was called the war-revolution thesis.

One of the notable thesis in the book was the necessity for Pakistan to acquire the fission weapon, and start a deterrence programme to be able to stand against the industrialised states, and against a nuclear armed India.

Penrose states that his ideas on the nature of consciousness are speculative, and his thesis is considered erroneous by experts in the fields of philosophy, computer science, and robotics.

Gurevich: "... Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage, an algorithm is a computational process defined by a Turing machine ".

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.

# REDIRECT Church – Turing thesis

In computability theory, the Church – Turing thesis ( also known as the Turing-Church thesis, the Church – Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis ) is a combined hypothesis (" thesis ") about the nature of functions whose values are effectively calculable ; or, in more modern terms, functions whose values are algorithmically computable.

The Church – Turing thesis is a statement that characterizes the nature of computation and cannot be formally proven.

Despite the fact that it has not been formally proven, the Church – Turing thesis now has near-universal acceptance.

Because all these different attempts at formalizing the concept of " effective calculability / computability " have yielded equivalent results, it is now generally assumed that the Church – Turing thesis is correct.

Proofs in computability theory often invoke the Church – Turing thesis in an informal way to establish the computability of functions while avoiding the ( often very long ) details which would be involved in a rigorous, formal proof.

The same thesis is implicit in Turing's description of computing machines (< sup > 23 </ sup >).

: Turing's thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i. e. by one of his machines, is equivalent to Church's thesis by Theorem XXX.

But a thesis concerning the extent of effective methods — which is to say, concerning the extent of procedures of a certain sort that a human being unaided by machinery is capable of carrying out — carries no implication concerning the extent of the procedures that machines are capable of carrying out, even machines acting in accordance with ' explicitly stated rules.

Defining what such game-playing machines mean, computability logic provides a generalization of the Church-Turing thesis to the interactive level.

The famous Church-Turing thesis attempts to define computation and computability in terms of Turing machines.

Kuhn's thesis showed various problems regarding the use of stack-based virtual machines for Perl, and this discovery became part of the justification for the launch of the Parrot project.

In her graduate thesis, Dayhoff had pioneered the use of computer capabilities — i. e., mass-data processing — to theoretical chemistry ; specifically, she applied punch card machines to calculate the resonance energies of several polycyclic organic molecules.

After joining the school, Couffignal hesitated to write a thesis on Symbolic Logic but after his meetings with Maurice d ' Ocagne, he decided to focus on machines and on Mechanical Logic.

Couffignal received his Doctorate of Sciences in 1938 with his thesis on Mechanical Analysis, demonstrating applications for machines to calculate celestial mechanics.

This work culminated in the theoretical development of so-called Turing machines and the Church – Turing thesis, which formalized the mathematics underlying computability theory.

* The St Piran Trust has undertaken research which has led them to the conclusion that Saint Piran was indeed Saint Ciarán of Saighir or perhaps a disciple, as indicated by Dr James Brennan of Kilkenny and Dr T. F. G. Dexter, whose thesis is held in the Royal Cornwall Museum.

In January 2001, during a visit to New York, IPN President Leon Kieres made public that IPN had accumulated enough evidence to confirm Gross ’ basic thesis that a group of Poles were indeed perpetrators in the Jedwabne massacre.

Scottish surgeon James Braid, who coined the term " hypnotism ", claimed that focused attention was essential for creating hypnotic trances ; indeed, his thesis was that hypnosis was in essence a state of extreme focus.

Brouwer then " embarked on a self-righteous campaign to reconstruct mathematical practice from the ground up so as to satisfy his philosophical convictions "; indeed his thesis advisor refused to accept his Chapter II " ' as it stands, ... all interwoven with some kind of pessimism and mystical attitude to life which is not mathematics, nor has anything to do with the foundations of mathematics ' " ( Davis, p. 94 quoting van Stigt, p. 41 ).

The historian Peter Hennessy quotes a PhD thesis by Michael Kandiah saying that Woolton was ' arguably the most successful of the Overlords ' partly because his ministries were quite closely related, indeed they were merged in 1955 as the Ministry of Agriculture, Fisheries and Food.

so all the inequalities are indeed equalities, and the thesis immediately follows.