Coherent functions and program checkers
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
On polynomial-time bounded truth-table reducibility of NP sets to sparse sets
SIAM Journal on Computing
On being incoherent without being very hard
Computational Complexity
Splittings, Robustness, and Structure of Complete Sets
SIAM Journal on Computing
Separating Complexity Classes Using Autoreducibility
SIAM Journal on Computing
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
Pseudo-Random Generators and Structure of Complete Degrees
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Separating Complexity Classes Using Structural Properties
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Autoreducibility, mitoticity, and immunity
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Autoreducibility, mitoticity, and immunity
Journal of Computer and System Sciences
The complexity of unions of disjoint sets
Journal of Computer and System Sciences
The Fault Tolerance of NP-Hard Problems
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
The complexity of unions of disjoint sets
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Space-efficient informational redundancy
Journal of Computer and System Sciences
The fault tolerance of NP-hard problems
Information and Computation
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We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glaßer et al. [12], complete sets for all of the following complexity classes are m-mitotic: NP, coNP, $\bigoplus$P, PSPACE, and NEXP, as well as all levels of PH, MODPH, and the Boolean hierarchy over NP. In the cases of NP, PSPACE, NEXP, and PH, this at once answers several well-studied open questions. These results tell us that complete sets share a redundancy that was not known before. In particular, every NP-complete set A splits into two NP-complete sets A1 and A2.