Variations on Muchnik's Conditional Complexity Theorem - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Theory of Computing Systems Year : 2011

Variations on Muchnik's Conditional Complexity Theorem


Muchnik's theorem about simple conditional descriptions states that for all strings a and b there exists a program p transforming a to b that has the least possible length and is simple conditional on b. In this paper we present two new proofs of this theorem. The first one is based on the on-line matching algorithm for bipartite graphs. The second one, based on extractors, can be generalized to prove a version of Muchnik's theorem for space-bounded Kolmogorov complexity. Another version of Muchnik's theorem is proven for a resource-bounded variant of Kolmogorov complexity based on Arthur-Merlin protocols.
Fichier principal
Vignette du fichier
csr-journal.pdf (224.51 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

lirmm-00736106 , version 1 (27-09-2012)



Daniil Musatov, Andrei Romashchenko, Alexander Shen. Variations on Muchnik's Conditional Complexity Theorem. Theory of Computing Systems, 2011, 9 (2), pp.227-245. ⟨10.1007/s00224-011-9321-z⟩. ⟨lirmm-00736106⟩
119 View
260 Download



Gmail Mastodon Facebook X LinkedIn More