Average case complete problems
SIAM Journal on Computing
The existence and density of generalized complexity cores
Journal of the ACM (JACM)
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
Journal of Computer and System Sciences
Fast Addition of Large Integers
IEEE Transactions on Computers
On the theory of average case complexity
Journal of Computer and System Sciences
Tight bounds on expected time to add correctly and add mostly correctly
Information Processing Letters
Information Processing Letters
A recursive introduction to the theory of computation
A recursive introduction to the theory of computation
An average complexity measure that yields tight hierarchies
Computational Complexity
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Fine Separation of Average-Time Complexity Classes
SIAM Journal on Computing
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
The Structure of Polynomial Complexity Cores (Extended Abstract)
Proceedings of the Mathematical Foundations of Computer Science 1984
Polynomial Time Samplable Distributions
MFCS '96 Proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Randomness vs. Time: De-Randomization under a Uniform Assumption
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic encryption & how to play mental poker keeping secret all partial information
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Towards average-case complexity analysis of NP optimization problems
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Average case computational complexity theory
Average case computational complexity theory
On approximating real-world halting problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We present two new complexity classes which are based on a complexity class C and an error probability function F. The first, F-Err C, reflects the (weak) feasibility of problems that can be computed within the error bound F. As a more adequate measure to investigate lower bounds we introduce F-Errio C where the error is infinitely often bounded by the function F. These definitions generalize existing models of feasible erroneous computations and cryptographic intractability. We identify meaningful bounds for the error function and derive new diagonalizing techniques. These techniques are applied to known time hierarchies to investigate the influence of error bound. It turns out that in the limit a machine with slower running time cannot predict the diagonal language within a significantly smaller error prob. than 1/2. Further, we investigate two classical non-recursive problems: the halting problem and the Kolmogorov complexity problem. We present strict lower bounds proving that any heuristic algorithm claiming to solve one of these problems makes unrecoverable errors with constant probability. Up to now it was only known that infinitely many errors will occur.