In computability theory , the Church—Turing thesis also known as computability thesis ,  the Turing—Church thesis ,  the Church—Turing conjecture , Church's thesis , Church's conjecture , and Turing's thesis is a hypothesis about the nature of computable functions. It states that a function on the natural numbers can be calculated by an effective method if and only if it is computable by a Turing machine. Before the precise definition of computable function, mathematicians often used the informal term effectively calculable to describe functions that are computable by paper-and-pencil methods. In the s, several independent attempts were made to formalize the notion of computability :. This has led mathematicians and computer scientists to believe that the concept of computability is accurately characterized by these three equivalent processes. Other formal attempts to characterize computability have subsequently strengthened this belief see below.
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A thesis THEE-ses is the main or controlling idea of an essay , report , speech , or research paper , sometimes written as a single declarative sentence known as a thesis statement. A thesis may be implied rather than stated directly. Plural: theses.
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