(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.
1982, Wolfgang Bibel, Automated Theorem Proving, End, DrG or Lew, is of the kind which we may expect, it is a semi-decision procedure which confirms if a formula is valid but may run forever for invalid formulas. Therefore, termination by running out of time or space after any finite number of steps will leave the question for the validity of a formula unsettled. ...
(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.)
