• Publications
  • Influence
A Downward Collapse within the Polynomial Hierarchy
TLDR
This paper provides an unqualified downward collapse result completely within the polynomial hierarchy and proves that, for k > 2, if P = 1, then P = 2, then $\Sigma^p_k = \Pi^p-k = {\rm PH}$. Expand
On claw-free asteroidal triple-free graphs
We present an O(n2.376) algorithm for recognizing claw-free AT-free graphs and a linear-time algorithm for computing the set of all central vertices of a claw-free AT-free graph. In addition, we giveExpand
Translating Equality Downwards
TLDR
A much broader downward translation of equality is provided that subsumes not only that downward translation but also that translation that was obtained that applied to the polynomial hierarchy to bounded access to its levels by Buhrman and Fortnow. Expand
A Downward Translation in the Polynomial Hierarchy
TLDR
This work provides an unqualified downward collapse result completely within the polynomial hierarchy, and proves that, for k < 2, if P^p_k[1] = P^{\sum^p-k[2] then P = PH, then p_k = Prod_k and this is extended to obtain a more general upward collapse result. Expand
The Operators min and max on the Polynomial Hierarchy
TLDR
This work defines a general maximization operator max and a general minimization operator min for complexity classes and shows that there are other interesting optimization classes beside OptP and is able to characterize the polynomial hierarchy uniformly by three operators. Expand
The Operators min and max on the Polynomial Hierarchy
TLDR
It turns out that a general max and a general min operator for complexity classes yield a refinement of Krentel's hierarchy of optimization functions, and it is proved that this refinement is strict unless the polynomial hierarchy collapses and show that the refinement is useful to exactly classify optimization functions. Expand
On Claw-Free Asteroidal Triple-Free Graphs
We present an O(n2.376) algorithm for recognizing claw-free AT-free graphs and a linear-time algorithm for computing the set of all central vertices of a claw-free AT-free graph. In addition, we giveExpand
Extending Downward Collapse from 1-versus-2 Queries to m-versus-m + 1 Queries
TLDR
The achievement of the k = 2 case cannot be strengthened to k = 1 by any relativizable proof technique, and the new downward translation obtained also tightens the collapse in the polynomial hierarchy implied by a collapse inThe bounded-query hierarchy of the second level of the polynnomial hierarchy. Expand
On Functions and Relations
TLDR
The approach sheds new light on well-studied classes like NPSV and NPMV, allows to give simpler proofs for known results, and shows that the spectrum of function classes closely resembles the Spectrum of well-known complexity classes. Expand
What's up with downward collapse: using the easy-hard technique to link Boolean and polynomial hierarchy collapses
TLDR
This article surveys the history, the results, and the method---the so-called easy-hard technique---of the just-mentioned nine-paper progression that achieves downward collapse within the polynomial hierarchy. Expand
...
1
2
3
4
5
...