different between noncomputable vs undecidable
noncomputable
English
Etymology
non- +? computable
Adjective
noncomputable (not comparable)
- (mathematics, of a function) Incapable of being computed by any deterministic algorithm in any finite amount of time.
Synonyms
- nonrecursive
Translations
noncomputable From the web:
- what does noncomputable mean
- what is non computable
undecidable
English
Etymology
un- +? decidable
Pronunciation
Adjective
undecidable (not comparable)
- (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. [...]
- The first-order procedure SP differs from the proposi-
- (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.)
Antonyms
- decidable
Related terms
- noncomputable
Translations
undecidable From the web:
- what are undecidable problems
- what is undecidable language
- what does undecidable mean
- what are undecidable problems in computer science
- what is undecidable problem in daa
- what is undecidable problem in algorithm
- what is undecidable problem in computability
- what does undecidable
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