DocumentCode :
1992431
Title :
Random strings make hard instances
Author :
Buhrman, Harry ; Orponen, Pekka
Author_Institution :
Dept. de Llenguatges i Sistemes Inf., Univ. Politecnica de Catalunya, Barcelona, Spain
fYear :
1994
fDate :
28 Jun- 1 Jul 1994
Firstpage :
217
Lastpage :
222
Abstract :
We establish the truth of the “instance complexity conjecture” in the case of DEXT-complete sets w.r.t. polynomial time computations, and r.e. complete sets w.r.t. recursive computations. Specifically, we obtain for every DEXT-complete set A an exponentially dense subset C such that for every nondecreasing polynomial t(n)=ω(n log n), ict(x:A)⩾Kt(x)-c holds for some constant c and all x∈C, where ict and Kt are the t-bounded instance complexity and Kolmogorov complexity measures, respectively. For r.e. complete sets A we obtain an infinite set C⊆A¯ such that ic(x:A)⩾K(x)-c holds for some constant c and all x∈C. The proofs are based on the observation that Kolmogorov random strings are individually hard to recognize by bounded computations
Keywords :
computational complexity; random number generation; DEXT-complete sets; Kolmogorov complexity measure; Kolmogorov random strings; bounded computations; bounded instance complexity; exponentially dense subset; instance complexity conjecture; nondecreasing polynomial; polynomial time computations; random strings; recursive computations; Computer science; Contracts; Polynomials; Postal services; Size measurement; Turing machines; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Structure in Complexity Theory Conference, 1994., Proceedings of the Ninth Annual
Conference_Location :
Amsterdam
Print_ISBN :
0-8186-5670-0
Type :
conf
DOI :
10.1109/SCT.1994.315802
Filename :
315802
Link To Document :
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