Category and measure in complexity classes
SIAM Journal on Computing
Complexity theory of real functions
Complexity theory of real functions
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Encyclopedic dictionary of mathematics (2nd ed.)
Encyclopedic dictionary of mathematics (2nd ed.)
Genericity and measure for exponential time
MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
Measure on P: strength of the notion
Information and Computation
The quantitative structure of exponential time
Complexity theory retrospective II
Genericity, Randomness, and Polynomial-Time Approximations
SIAM Journal on Computing
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Resource-bounded Baire category: a stronger approach
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Measure on small complexity classes, with applications for BPP
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
On the size of sets of computable functions
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
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A notion of resource-bounded Baire category is developed for the class PC[0,1] of all polynomial-time computable real-valued functions on the unit interval. The meager subsets of PC[0,1] are characterized in terms of resource-bounded Banach-Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function in PC[0,1] is nowhere differentiable. This is a complexity-theoretic extension of the analogous classical result that Banach proved for the class C[0, 1] in 1931.