undecidable

英語（米国） (en-US) 英語（イギリス） (en-GB)

形容詞

比較不可

(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.

日本語の意味

数学や計算理論において、有限な時間内でアルゴリズムによって解決（決定）できない性質を持つこと。 / 有限のステップで正確な判断や決定が不可能な問題や集合に対して用いられる。

英語の意味

(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.

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The halting problem is a classic example of an undecidable decision problem in computability theory.

停止問題は計算理論における、有限時間でいかなるアルゴリズムでも判定できない決定問題の代表的な例です。

詳細

意味（1）

(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.

The first-order procedure SP differs from the proposi- tional procedure CP°₁ in an essential feature. Namely, CP°₁ always terminates while SP may run forever as we have seen with the example immediately after (3.7). This is not a specific defect of SP. Rather it is known that first-order logic is an undecidable theory while propositional logic is a decidable theory. This means that for the latter there are decision pro- cedures which for any formula decide whether it is valid or not — and CP°₁ in fact is such a decision procedure — while for the former such decision procedures do not exist in princi- ple. Thus SP, according to these results for which the reader is referred to any logic texts such as [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. …

詳細

意味（2）

(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.)