undecidable

  1. Adjective.  (mathematics, computing theory) Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
  2. Adjective.  (mathematics) (''of a WFF'') logically independent from the axioms of a given theory; i.e., that it can ''never'' be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (''Note:'' this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.).

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This entry was last updated on RefTopia from its source on 3/20/2012.