computability theory

(mathematics)The area of theoretical computer scienceconcerning what problems can be solved by any computer.

A function is computable if an algorithm can be implementedwhich will give the correct output for any valid input.

Since computer programs are countable but real numbers arenot, it follows that there must exist real numbers thatcannot be calculated by any program. Unfortunately, bydefinition, there isn't an easy way of describing any of them!

In fact, there are many tasks (not just calculating realnumbers) that computers cannot perform. The most well-knownis the halting problem, the busy beaver problem is lessfamous but just as fascinating.

["Computability", N.J. Cutland. (A well writtenundergraduate-level introduction to the subject)].

["The Turing Omnibus", A.K. Dewdeney].

单词	computability theory
释义	DictionarySeecomputable computability theory computability theory (mathematics)The area of theoretical computer scienceconcerning what problems can be solved by any computer. A function is computable if an algorithm can be implementedwhich will give the correct output for any valid input. Since computer programs are countable but real numbers arenot, it follows that there must exist real numbers thatcannot be calculated by any program. Unfortunately, bydefinition, there isn't an easy way of describing any of them! In fact, there are many tasks (not just calculating realnumbers) that computers cannot perform. The most well-knownis the halting problem, the busy beaver problem is lessfamous but just as fascinating. ["Computability", N.J. Cutland. (A well writtenundergraduate-level introduction to the subject)]. ["The Turing Omnibus", A.K. Dewdeney].
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