ERRATUM: the polynomial time hierarchy collapses if the boolean hierarchy collapses
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It is shown that if the Boolean hierarchy (BH) collapses, then there exists a sparse set S such that ${\text{co-NP}} \subseteq {\text{ NP}}^S $, and therefore the polynomial time hierarchy (PH) col...Abstract:
It is shown that if the Boolean hierarchy (BH) collapses, then there exists a sparse set S such that ${\text{co-NP}} \subseteq {\text{ NP}}^S $, and therefore the polynomial time hierarchy (PH) col...read more
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Journal Article
Query Order and the Polynomial Hierarchy
TL;DR: It is proved that all leaf language classes - and thus essentially all standard complexity classes - inherit all order-obliviousness results that hold for P. complexity levels, and it is shown that these ordered query classes form new levels in the polynomial hierarchy unless the poynomial hierarchy collapses.
Dissertation
The Domatic Number Problem: Boolean Hierarchy Completeness and Exact Exponential-Time Algorithms
TL;DR: Das Domatic Number Problem wird in verschiedenen Variationen aus komplexitatstheoretischer Sicht betrachtet anderswo die hoheren Stufen der Booleschen Hierarchie uber NP erzielt.
Journal Article
Extending downward collapse from 1-versus-2 queries to j-versus-j + 1 queries
TL;DR: The achievement of the k = 2 case is unlikely to be strengthened to k = 1 any time in the foreseeable future, but the new downward translation obtained tightens the collapse in the polynomial hierarchy implied by a collapses in the bounded-query hierarchy of the second level of the poynomial hierarchy.
Posted Content
Exact Complexity of Exact-Four-Colorability
TL;DR: In this paper, it was shown that the problem of determining the chromatic number of a given graph is DP-complete for any given set of elements of the set of non-contiguous integers.
Book ChapterDOI
On checking versus evaluation of multiple queries
TL;DR: Companion theories—both complexity-theoretic and recursion- theoretic—of characteristic vector terseness are developed, which ask whether the answers to many membership queries to a hard set can be checked with fewer queries.
References
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Journal ArticleDOI
The polynomial-time hierarchy☆
TL;DR: The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established.
Journal ArticleDOI
Nondeterministic space is closed under complementation
TL;DR: It immediately follows that the context-sensitive languages are closed under complementation, thus settling a question raised by Kuroda.
Proceedings ArticleDOI
Some connections between nonuniform and uniform complexity classes
TL;DR: This work aims to understand when nonuniform upper bounds can be used to obtain uniform upper bounds, and how to relate it to more common notions.
Journal ArticleDOI
On Isomorphisms and Density of $NP$ and Other Complete Sets
Leonard Berman,Juris Hartmanis +1 more
TL;DR: It is shown that complete sets in EXPTIME and EXPTAPE cannot be sparse and therefore they cannot be over a single letter alphabet, and the hardest context-sensitive languages can be sparse.
Journal ArticleDOI
A comparison of polynomial time reducibilities
TL;DR: Various forms of polynomial time reducibility are compared.