Recursively enumerable in the context of Computability theory

⭐ Core Definition: Recursively enumerable

In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable, provable or Turing-recognizable if:

There is an algorithm such that the set of input numbers for which the algorithm halts is exactly S.

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Recursively enumerable in the context of Davis–Putnam algorithm

In logic and computer science, the Davis–Putnam algorithm was developed by Martin Davis and Hilary Putnam for checking the validity of a first-order logic formula using a resolution-based decision procedure for propositional logic. Since the set of valid first-order formulas is recursively enumerable but not recursive, there exists no general algorithm to solve this problem. Therefore, the Davis–Putnam algorithm only terminates on valid formulas. Today, the term "Davis–Putnam algorithm" is often used synonymously with the resolution-based propositional decision procedure (Davis–Putnam procedure) that is actually only one of the steps of the original algorithm.

View the full Wikipedia page for Davis–Putnam algorithm

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Recursively enumerable in the context of Computability theory

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⭐ Core Definition: Recursively enumerable

Recursively enumerable in the context of Davis–Putnam algorithm