The complexity of promise problems with applications to public-key cryptography
Information and Control
Average case complete problems
SIAM Journal on Computing
Probalisitic complexity classes and lowness
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Random-self-reducibility of complete sets
SIAM Journal on Computing
Journal of Computer and System Sciences
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Randomness-optimal sampling, extractors, and constructive leader election
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Resource-Bounded Kolmogorov Complexity Revisited
SIAM Journal on Computing
SIAM Journal on Computing
Polynomial Time Samplable Distributions
MFCS '96 Proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science
Cryptocomplexity and NP-Completeness
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Sets Computable in Polynomial Time on Average
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Average case computational complexity theory
Average case computational complexity theory
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
One-sided versus two-sided error in probabilistic computation
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
| Hi-index | 0.00 |
We study polynomial-time randomized algorithms that solve problems on "most" inputs with "small" error probability. The sets that have such algorithms are called nearly BPP sets, which naturally expand BPP sets. Notably, sparse sets and average BPP sets are typical examples of nearly BPP sets. It is, however, open whether all NP sets are nearly BPP. The nearly BPP sets can be captured by Nisan-Wigderson's approximation scheme as well as viewed as a special case of promise BPP problems. Moreover, nearly BPP sets are precisely described in terms of Sipser's distinguishing complexity. These sets have a connection to average-case complexity and cryptography. Nevertheless, unlike BPP, the class of nearly BPP sets is not closed even under honest polynomial-time one-one reductions. In this paper, we study a more general notion of nearly BP[C] sets, analogous to Schöning's probabilistic class BP[C] for any complexity class C. The "infinitely-often" version of nearly BPP sets shows a direct connection to cryptographic one-way partial functions.