Compression theorem

Compression theorem In computational complexity theory, the compression theorem is an important theorem about the complexity of computable functions.

The theorem states that there exists no largest complexity class, with computable boundary, which contains all computable functions.

Compression theorem Given a Gödel numbering {stile di visualizzazione varphi } of the computable functions and a Blum complexity measure {stile di visualizzazione Phi } where a complexity class for a boundary function {stile di visualizzazione f} is defined as {displaystyle matematica {C} (f):={varfi _{io}in matematica {R} ^{(1)}|(forall ^{infty }X),Phi _{io}(X)leq f(X)}.} Then there exists a total computable function {stile di visualizzazione f} so that for all {stile di visualizzazione i} {displaystyle matematica {Dom} (varfi _{io})= matematica {Dom} (varfi _{f(io)})} e {displaystyle matematica {C} (varfi _{io})subsetneq mathrm {C} (varfi _{f(io)}).} References Salomaa, Arto (1985), "Teorema 6.9", Computation and Automata, Enciclopedia della matematica e sue applicazioni, vol. 25, Cambridge University Press, pp. 149–150, ISBN 9780521302456. Zimand, Marius (2004), "Teorema 2.4.3 (Compression theorem)", Complessità computazionale: A Quantitative Perspective, Studi di matematica dell'Olanda settentrionale, vol. 196, Altro, p. 42, ISBN 9780444828415. P ≟ NP This theoretical computer science–related article is a stub. Puoi aiutare Wikipedia espandendolo.

Categorie: Computational complexity theoryStructural complexity theoryTheorems in the foundations of mathematicsTheoretical computer science stubs