The geometry of fractal sets
On encoding and decoding with two-way head machines
Information and Computation
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
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
Hausdorff Dimension in Exponential Time
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Weighted finite automata and metrics in cantor space
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Note: fractal dimension and logarithmic loss unpredictability
Theoretical Computer Science
Dimension in Complexity Classes
SIAM Journal on Computing
The dimensions of individual strings and sequences
Information and Computation
Theoretical Computer Science
Effective fractal dimension: foundations and applications
Effective fractal dimension: foundations and applications
Scaled dimension and nonuniform complexity
Journal of Computer and System Sciences
Journal of Computer and System Sciences - Special issue on COLT 2002
Entropy rates and finite-state dimension
Theoretical Computer Science
Selection Functions that Do Not Preserve Normality
Theory of Computing Systems
A note on dimensions of polynomial size circuits
Theoretical Computer Science
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Online Learning and Resource-Bounded Dimension: Winnow Yields New Lower Bounds for Hard Sets
SIAM Journal on Computing
Effective Strong Dimension in Algorithmic Information and Computational Complexity
SIAM Journal on Computing
Partial Bi-immunity, Scaled Dimension, and NP-Completeness
Theory of Computing Systems
Dimension Characterizations of Complexity Classes
Computational Complexity
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
Extracting kolmogorov complexity with applications to dimension zero-one laws
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Autoreducibility, mitoticity, and immunity
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Generic density and small span theorem
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Hardness hypotheses, derandomization, and circuit complexity
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Compression of individual sequences via variable-rate coding
IEEE Transactions on Information Theory
Gambling using a finite state machine
IEEE Transactions on Information Theory
| Hi-index | 5.23 |
Resource-bounded dimension is a notion of computational information density of infinite sequences based on computationally bounded gamblers. This paper develops the theory of pushdown dimension and explores its relationship with finite-state dimension. The pushdown dimension of any sequence is trivially bounded above by its finite-state dimension, since a pushdown gambler can simulate any finite-state gambler. We show that for every rational 0