A Kolmogorov complexity characterization of constructive Hausdorff dimension
Information Processing Letters
MAX3SAT is exponentially hard to approximate if NP has positive dimension
Theoretical Computer Science
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Correspondence Principles for Effective Dimensions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Gales and the Constructive Dimension of Individual Sequences
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
Gales suffice for constructive dimension
Information Processing Letters
Scaled dimension and nonuniform complexity
Journal of Computer and System Sciences
SIGACT news complexity theory column 48
ACM SIGACT News
Journal of Computer and System Sciences - Special issue on COLT 2002
Generic density and small span theorem
Information and Computation
Martingale families and dimension in P
Theoretical Computer Science
Effective Dimensions and Relative Frequencies
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Kolmogorov-Loveland stochasticity and Kolmogorov complexity
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
The dynamics of cellular automata in shift-invariant topologies
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Every sequence is decompressible from a random one
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Martingale families and dimension in p
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Generic density and small span theorem
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
The dimension of a point: computability meets fractal geometry
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
| Hi-index | 0.01 |
A theory of resource-bounded dimension is developed using gales, which are natural generalizations of martin-gales. When the resource bound \math (a parameter of the theory) is unrestricted, the resulting dimension is precisely the classical Hausdorff dimension (sometimes called 驴fractal dimension驴). Other choices of the parameter \math yield internal dimension theories in E, E2, ESPACE, and other complexity classes, and in the class of all decidable problems.In general, if C is such a class, then every set X of languages has a dimension in C, which is a real number dim\math. Along with the elements of this theory, two preliminary applications are presented: 1. For every real number \math , the set FREQ(\math), consisting of all languages that asymptotically contain at most \math of all strings, has dimension H(\math) - the binary entropy of \math -in E and in E2. 2. For every real number \math, the set SIZE(\math), consisting of all languages decidable by Boolean circuits of at most \math gates, has dimension \math in ESPACE.