Decidable vs Undecidable - What's the difference?
decidable | undecidable | Antonyms |
capable of being decided.
(computer science) describing a set for which there exists an algorithm that will determine whether any element is or is not within the set in a finite amount of time.
(logic) in intuitionistic logic, a proposition P'' is decidable in a given theory if it can be proven from the theory that "either ''P'' or not ''P ", i.e. in symbols: .http://plato.stanford.edu/entries/logic-intuitionistic/
(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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(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.)
Undecidable is an antonym of decidable.
Decidable is an antonym of undecidable.
As adjectives the difference between decidable and undecidable
is that decidable is capable of being decided while undecidable is (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.decidable
English
Adjective
(en adjective)- It is easy to show that the set of even numbers is decidable by creating the relevant Turing machine.
Synonyms
* (computer science) recursive, computableAntonyms
* undecidableDerived terms
* semi-decidableReferences
undecidable
English
Adjective
(-)- 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. [...]
