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A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be noted that an unsolvable problem might be partially solvable by an algorithm that makes a complete search for a solution. In such case the solution is eventually found whenever it is defined, but the search might continue forever whenever the solution is undefined. Similarly, an undecidable problem might also be partially decidable by an algorithm that makes an exhaustive search.
When we study computability we are studying problems in an abstract sense. For example, addition is the problem of, having been given two numbers, returning a third number that is
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One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define part
Computations are deliberate for processing information. Computability theory was discovered in the 1930s, and extended in the 1950s and 1960s. Its basic ideas have become part of
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