Formal Definition of Many-One Reduction (≤m )
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Introduction & Overview
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Quick Overview
A **many-one reduction (<=m) from language A to language B** means that there exists a total computable function f (a "reduction function") such that any string w is in language A if and only if the transformed string f(w) is in language B. This function f must be computable by a Turing Machine that always halts. This formal definition underpins the powerful technique used to prove the undecidability of problems: if problem A is known to be undecidable and can be many-one reduced to problem B, then problem B must also be undecidable.