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Abstract: This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time, many-one reductions. It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity. It follows that every weakly hard problem has a dense set of such maximally hard instances. This extends the theorem, due to Orponen, Ko, Schoning and Watanabe (1994), that every hard problem for exponential... (Update)
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BibTeX entry: (Update)
@article{ lutz00hard,
author = "Jack H. Lutz and Vikram Mhetre and Sridhar Srinivasan",
title = "Hard Instances of Hard Problems",
journal = "Lecture Notes in Computer Science",
volume = "1770",
pages = "324--??",
year = "2000",
url = "citeseer.ist.psu.edu/704040.html" }
Citations (may not include all citations):2319 Elements of Information Theory (context) - Cover, Thomas - 1991
660 An Introduction to Kolmogorov Complexity and its Application.. - Li, Vit'anyi - 1997
169 A formal theory of inductive inference (context) - Solomonoff - 1964
142 Almost everywhere high nonuniform complexity - Lutz - 1992
126 On isomorphism and density of NP and other complete sets (context) - Berman, Hartmanis - 1977
120 the length of programs for computing finite binary sequences.. - Chaitin - 1969
71 The quantitative structure of exponential time - Lutz - 1997
49 Almost every set in exponential time is P-bi-immune - Mayordomo - 1994
47 Zufalligkeit und Wahrscheinlichkeit (context) - Schnorr - 1971
42 The complexity and distribution of hard problems - Juedes, Lutz - 1995
40 Process complexity and effective random tests (context) - Schnorr - 1973
35 Etude critique de la notion de collectif (context) - Ville - 1939
33 Cook versus Karp-Levin: Separating completeness notions if N.. - Lutz, Mayordomo - 1996
33 A unified approach to the definition of random sequences (context) - Schnorr - 1971
30 Resource-bounded measure (context) - Lutz - 1998
29 Theoretical Computer Science (context) - Juedes, Lutz et al. - 1995
25 Structural Complexity II (context) - Balc'azar, D'iaz et al. - 1990
24 On resource-bounded instance complexity - Fortnow, Kummer - 1996
19 On reducibility to complex or sparse sets (context) - Lynch - 1975
19 Resource-bounded measure and randomness (context) - Ambos-Spies, Mayordomo - 1997
17 Klassifikation der Zufallsgesetze nach Komplexitat und Ordnu.. (context) - Schnorr - 1970
17 The density and complexity of polynomial cores for intractab.. (context) - Orponen, Schoning - 1986
13 Resource bounded randomness and weakly complete problems (context) - Ambos-Spies, Terwijn et al. - 1997
12 Random strings make hard instances - Buhrman, Orponen - 1996
12 the complexity of random strings (context) - Kummer - 1996
11 of Information (context) - Kolmogorov, to et al. - 1965
11 An excursion to the Kolmogorov random strings - Buhrman, Mayordomo - 1997
11 Bi-immune sets for complexity classes (context) - Balc'azar, Schoning - 1985
10 The existence and density of generalized complexity cores (context) - Book, Du - 1987
8 On polynomial and generalized complexity cores (context) - Book, Du et al. - 1988
8 Complete sets and structure in subrecursive classes - Buhrman, Torenvliet - 1998
7 A note on the instance complexity of pseudorandom sets (context) - Ko - 1992
6 Hard core theorems for complexity classes (context) - Even, Selman et al. - 1985
5 A classification of complexity core lattices (context) - Orponen - 1986
5 and the distribution of hardness (context) - Juedes, Lutz et al. - 1992
5 On solving hard problems by polynomial-size circuits (context) - Huynh - 1987
4 On inefficient special cases of np-complete problems (context) - Du, Book - 1989
4 Journal of the Association of Computing Machinery (context) - Orponen, Ko et al. - 1994
4 Mathematical Systems Theory (context) - Russo, Orponen et al. - 1987
4 Generalized complexity cores and levelability of intractable.. (context) - Du - 1985
3 NP-hard sets have many hard instances (context) - Mundhenk - 1997
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