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Hypercomputation
Hypercomputation or super-Turing computation refers to models of computation that can provide outputs that are not Turing-computable. Super-Turing computing, introduced at the early 1990's by Hava Siegelmann, refers to such neurological inspired, biological and physical realizable computing; It became the mathematical foundations of Lifelong Machine Learning. Hypercomputation, introduced as a field of science in the late 1990s, is said to be based on the Super Turing but it also includes constructs which are philosophical. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that can correctly evaluate every statement in Peano arithmetic. The Church–Turing thesis states that any "computable" function that can be computed by a mathematician with a pen and paper using a finite set of simple algorithms, can be computed by a Turing machine. Hypercomputers compute functions that a Turing machine cannot and which are, hence, not computa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing-computable
Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can return the corresponding output. Computable functions are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions. Particular models of computability that give rise to the set of computable functions are the Turing-computable functions and the general recursive functions. Before the precise definition of computable function, mathematicians often used the informal term ''effectively calculable''. This term has since come to be identified with the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |