Reducibility in a sentence

A technical detail not discussed here but required to complete the proof is immersion reducibility.

Axiom of infinity Ramified types and the axiom of reducibility In simple type theory objects are elements of various disjoint "types".

But reducibility was required to be sure that the formal statements even properly express statements of real analysis, so that statements depending on it could not be reformulated as conditionals.

Frank P. Ramsey tried to argue that Russell's ramification of the theory of types was unnecessary, so that reducibility could be removed, but these arguments seemed inconclusive.

Here methods like random self-reducibility can be used for some specific problems to show that the worst case is no harder than the average case, or, equivalently, that the average case is no easier than the worst case.

Now equipped with the matrix notion, PM can assert its controversial axiom of reducibility : a function of one or two variables (two being sufficient for PM 's use) where all its values are given (i.

Regardless of the reducibility properties of a generator polynomial of degree r, if it includes the "+1" term, the code will be able to detect error patterns that are confined to a window of r contiguous bits.

Self-reducibility The SAT problem is self-reducible, that is, each algorithm which correctly answers if an instance of SAT is solvable can be used to find a satisfying assignment.

The concept of semisimplicity for Lie algebras is closely related with the complete reducibility (semisimplicity) of their representations.

The first of these is local consistency, also known as local reducibility, which says that any derivation containing an introduction of a connective followed immediately by its elimination can be turned into an equivalent derivation without this detour.

The formalisation defines algorithm complexity, problem complexity and reducibility which in turn allows equivalence classes to be defined.

They also had to make several compromises in order to develop so much of mathematics, such as an " axiom of reducibility ".

This includes six primitive propositions ✸9 through ✸9.15 together with the Axioms of reducibility.

This means essentially the lack of any particular reduction strategy—with regard to reducibility, "all bets are off".

Wittgenstein 1919, 1939 By the second edition of PM, Russell had removed his axiom of reducibility to a new axiom (although he does not state it as such).