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 {Anzeigestil Varphi } of the computable functions and a Blum complexity measure {Anzeigestil Phi } where a complexity class for a boundary function {Anzeigestil f} is defined as {Anzeigestil mathrm {C} (f):={varphi_{ich}in mathbf {R} ^{(1)}|(forall ^{unendlich }x),Phi_{ich}(x)leq f(x)}.} Then there exists a total computable function {Anzeigestil f} so that for all {Anzeigestil i} {Anzeigestil mathrm {Dom} (varphi_{ich})=mathrm {Dom} (varphi_{f(ich)})} und {Anzeigestil mathrm {C} (varphi_{ich})subsetneq mathrm {C} (varphi_{f(ich)}).} References Salomaa, Arto (1985), "Satz 6.9", Computation and Automata, Enzyklopädie der Mathematik und ihrer Anwendungen, vol. 25, Cambridge University Press, pp. 149–150, ISBN 9780521302456. Zimand, Marius (2004), "Satz 2.4.3 (Compression theorem)", Rechenkomplexität: A Quantitative Perspective, Nordholländisches Mathematikstudium, vol. 196, Elsevier, p. 42, ISBN 9780444828415. P ≟ NP This theoretical computer science–related article is a stub. Sie können Wikipedia helfen, indem Sie es erweitern.

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