Informasjon om | Engelsk ordet UNDECIDABLE

Eksempler på bruk av UNDECIDABLE i en setning

• In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable.
• However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP-hard (unless P=NP).
• An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two-dimensional figure which is instantly and naturally understood as representing a projection of a three-dimensional object but cannot exist as a solid object.
• The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946.
• Due to many forms of static analysis being computationally undecidable, the mechanisms for performing it may not always terminate with the correct answer.
• Also provably unsolvable are so-called undecidable problems, such as the halting problem for Turing machines.
• Verifying sequential consistency through model checking is undecidable in general, even for finite-state cache coherence protocols.
• The set of Gödel numbers of arithmetic proofs described in Kurt Gödel's paper "On formally undecidable propositions of Principia Mathematica and related systems I" is computable; see Gödel's incompleteness theorems.
• An extension of the halting problem is called Rice's theorem, which states that it is undecidable (in general) whether a given language possesses any specific nontrivial property.
• However, logical implication between dependencies that can be inclusion dependencies or functional dependencies is undecidable by reduction from the word problem for monoids.
• The problem of whether a given context-free language is linear is shown to be recursively undecidable.
• A statement is independent of ZFC (sometimes phrased "undecidable in ZFC") if it can neither be proven nor disproven from the axioms of ZFC.
• Q is finitely axiomatizable because it lacks Peano arithmetic's axiom schema of induction; nevertheless Q, like Peano arithmetic, is incomplete and undecidable in the sense of Gödel.
• Likewise, a reduction computing a noncomputable function can reduce an undecidable problem to a decidable one.
• Unfortunately, making this intuition precise is subtle and mostly yields unwieldy characterisations of equality (which in most cases must also be undecidable, as a consequence of the halting problem).
• For instance, the general question of equality of two functions is equivalent to the halting problem, and is undecidable, but equality of two functions in FP is just equality in the algebra, and thus (Backus imagines) easier.
• For example, there are undecidable theories in propositional logic, although the set of validities (the smallest theory) is decidable.
• Deciding on extensional equality is undecidable in general and even for functions with finite domains often intractable.
• The truth or falsity of this hypothesis is undecidable and cannot be proven within the widely used Zermelo–Fraenkel set theory with axiom of choice (ZFC).
• Huet showed in 1973 that 3rd order unification is undecidable and this was improved upon by Baxter in 1978 then by Goldfarb in 1981 by showing that 2nd order unification is already undecidable.

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