Quantitative relativizations of complexity classes
SIAM Journal on Computing
Complexity classes without machines: on complete languages for UP
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
The Boolean hierarchy: hardware over NP
Proc. of the conference on Structure in complexity theory
Exponential time and bounded arithmetic
Proc. of the conference on Structure in complexity theory
On sparse oracles separating feasible complexity classes
3rd annual symposium on theoretical aspects of computer science on STACS 86
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of quasigroup isomorphism and the minimum generating set problem
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
| Hi-index | 0.00 |
The polynomial hierarchy, composed of the levels P, NP, PNP, NPNP, etc., plays a central role in classifying the complexity of feasible computations. It is not known whether the polynomial hierarchy collapses.We resolve the question of collapse for an exponential-time analogue of the polynomial-time hierarchy. Composed of the levels E (i.e., ⋓c DTIME[2cn]), NE, PNE, NPNE, etc., the strong exponential hierarchy collapses to its &Dgr;2 level. E ≠ PNE = NPNE ⋓ NPNPNE ⋓ ··· Our proof stresses the use of partial census information and the exploitation of nondeterminism.Extending our techniques, we also derive new quantitative relativization results. We show that if the (weak) exponential hierarchy's &Dgr;j+1 and &Sgr;j+1 levels, respectively E&Sgr;pj and NE&Sgr;pj, do separate, this is due to the large number of queries NE makes to its &Sgr;pj database.1Our technique provide a successful method of proving the collapse of certain complexity classes.