A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
An Overview of the Theory of Computational Complexity
Journal of the ACM (JACM)
On Reducibility to Complex or Sparse Sets
Journal of the ACM (JACM)
Comparison of polynomial-time reducibilities
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Formal languages and their relation to automata
Formal languages and their relation to automata
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Properties of sets which are complex because they encode complexity classes areexplored. It is shown that not all sets with inherent complexity are of this type, although this is the only type of set for which well-developed techniques exist for proving inherent complexity. Possibilities for the complexity of encoding sets are discussed, first with referenceto an ''almost everywhere'' vs. ''infinitely many arguments'' classification, and later with reference to the density of the set of arguments on which the problem is complex. It is shown that relative complexity relationships among sets of this type are highlystructured, in contrast to the wide variation possible among arbitrary recursive sets.