On total functions, existence theorems and computational complexity
Theoretical Computer Science
A general method to construct oracles realizing given relationships between complexity classes
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Information and Computation
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Information and Computation
Separability and one-way functions
Computational Complexity
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)
The Shrinking Property for NP and coNP
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
The shrinking property for NP and coNP
Theoretical Computer Science
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The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomial-time does this imply the polynomial-time hierarchy collapses? (By computing a multivalued function in deterministic polynomial-time we mean on every input producing one of the possible values of that function on that input.) We give a relativized negative answer to this question by exhibiting an oracle under which TFNP functions are easy to compute but the polynomial-time hierarchy is infinite. We also show that relative to this same oracle, P ≠ UP and TFNPNP functions are not computable in polynomial-time with an NP oracle.