Baire Category and Nowhere Differentiability for Feasible Real Functions
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Category, Measure, Inductive Inference: A Triality Theorem and Its Applications
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Separating NP-Completeness Notions Under Strong Hypotheses
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Generic density and small span theorem
Information and Computation
Baire categories on small complexity classes and meager--comeager laws
Information and Computation
Automatic forcing and genericity: on the diagonalization strength of finite automata
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
| Hi-index | 0.00 |
The paper introduces a new definition of resource-bounded Baire category in the style of Lutz (1987, 1990, 1992) . This definition gives an almost-all/almost-none theory of various complexity classes. The meagerness/comeagerness of many more classes can be resolved in the new definition than in previous definitions. For example, almost no sets in EXP are EXP-complete, and NP is PF-meager unless NP=EXP. It is also seen under the new definition that no rec-random set can be (recursively) tt-reducible to any PF-generic set. We weaken our definition by putting arbitrary bounds on the length of extension strategies, obtaining a spectrum of different theories of Baire category that includes Lutz's original definition.