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REPORTS > AUTHORS > DIETER VAN MELKEBEEK:
All reports by Author Dieter van Melkebeek:

TR17-158 | 23rd October 2017
Eric Allender, Joshua Grochow, Dieter van Melkebeek, Cris Moore, Andrew Morgan

Minimum Circuit Size, Graph Isomorphism, and Related Problems

We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted as MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions ... more >>>


TR17-052 | 19th March 2017
Dieter van Melkebeek, Gautam Prakriya

Derandomizing Isolation in Space-Bounded Settings

We study the possibility of deterministic and randomness-efficient isolation in space-bounded models of computation: Can one efficiently reduce instances of computational problems to equivalent instances that have at most one solution? We present results for the NL-complete problem of reachability on digraphs, and for the LogCFL-complete problem of certifying acceptance ... more >>>


TR12-080 | 18th June 2012
Baris Aydinlioglu, Dieter van Melkebeek

Nondeterministic Circuit Lower Bounds from Mildly Derandomizing Arthur-Merlin Games

In several settings derandomization is known to follow from circuit lower bounds that themselves are equivalent to the existence of pseudorandom generators. This leaves open the question whether derandomization implies the circuit lower bounds that are known to imply it, i.e., whether the ability to derandomize in *any* way implies ... more >>>


TR11-158 | 25th November 2011
Matthew Anderson, Dieter van Melkebeek, Nicole Schweikardt, Luc Segoufin

Locality from Circuit Lower Bounds

We study the locality of an extension of first-order logic that captures graph queries computable in AC$^0$, i.e., by families of polynomial-size constant-depth circuits. The extension considers first-order formulas over relational structures which may use arbitrary numerical predicates in such a way that their truth value is independent of the ... more >>>


TR10-188 | 8th December 2010
Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich

Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae

Revisions: 1

We present a polynomial-time deterministic algorithm for testing whether constant-read multilinear arithmetic formulae are identically zero. In such a formula each variable occurs only a constant number of times and each subformula computes a multilinear polynomial. Our algorithm runs in time $s^{O(1)}\cdot n^{k^{O(k)}}$, where $s$ denotes the size of the ... more >>>


TR10-174 | 12th November 2010
Scott Aaronson, Baris Aydinlioglu, Harry Buhrman, John Hitchcock, Dieter van Melkebeek

A note on exponential circuit lower bounds from derandomizing Arthur-Merlin games

We present an alternate proof of the recent result by Gutfreund and Kawachi that derandomizing Arthur-Merlin games into $P^{NP}$ implies linear-exponential circuit lower bounds for $E^{NP}$. Our proof is simpler and yields stronger results. In particular, consider the promise-$AM$ problem of distinguishing between the case where a given Boolean circuit ... more >>>


TR10-147 | 22nd September 2010
Dieter van Melkebeek, Thomas Watson

Time-Space Efficient Simulations of Quantum Computations

Revisions: 1

We give two time- and space-efficient simulations of quantum computations with
intermediate measurements, one by classical randomized computations with
unbounded error and the other by quantum computations that use an arbitrary
fixed universal set of gates. Specifically, our simulations show that every
language solvable by a bounded-error quantum algorithm running ... more >>>


TR10-129 | 16th August 2010
Jeff Kinne, Dieter van Melkebeek, Ronen Shaltiel

Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds

The area of derandomization attempts to provide efficient deterministic simulations of randomized algorithms in various algorithmic settings. Goldreich and Wigderson introduced a notion of "typically-correct" deterministic simulations, which are allowed to err on few inputs. In this paper we further the study of typically-correct derandomization in two ways.

First, we ... more >>>


TR10-105 | 29th June 2010
Scott Aaronson, Dieter van Melkebeek

A note on circuit lower bounds from derandomization

We present an alternate proof of the result by Kabanets and Impagliazzo that derandomizing polynomial identity testing implies circuit lower bounds. Our proof is simpler, scales better, and yields a somewhat stronger result than the original argument.

more >>>

TR10-038 | 10th March 2010
Dieter van Melkebeek, Holger Dell

Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses

Revisions: 1

Consider the following two-player communication process to decide a language $L$: The first player holds the entire input $x$ but is polynomially bounded; the second player is computationally unbounded but does not know any part of $x$; their goal is to cooperatively decide whether $x$ belongs to $L$ at small ... more >>>


TR08-017 | 16th December 2007
Thomas Watson, Dieter van Melkebeek

A Quantum Time-Space Lower Bound for the Counting Hierarchy

We obtain the first nontrivial time-space lower bound for quantum algorithms solving problems related to satisfiability. Our bound applies to MajSAT and MajMajSAT, which are complete problems for the first and second levels of the counting hierarchy, respectively. We prove that for every real $d$ and every positive real $\epsilon$ ... more >>>


TR07-134 | 14th December 2007
Jeff Kinne, Dieter van Melkebeek

Space Hierarchy Results for Randomized and Other Semantic Models

Revisions: 1

We prove space hierarchy and separation results for randomized and other semantic models of computation with advice. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the following.

Let <i>s</i>(<i>n</i>) ... more >>>


TR07-099 | 30th September 2007
Dieter van Melkebeek

A Survey of Lower Bounds for Satisfiability and Related Problems

Ever since the fundamental work of Cook from 1971, satisfiability has been recognized as a central problem in computational complexity. It is widely believed to be intractable, and yet till recently even a linear-time, logarithmic-space algorithm for satisfiability was not ruled out. In 1997 Fortnow, building on earlier work by ... more >>>


TR05-111 | 3rd October 2005
Dieter van Melkebeek, Konstantin Pervyshev

A Generic Time Hierarchy for Semantic Models With One Bit of Advice

We show that for any reasonable semantic model of computation and for
any positive integer $a$ and rationals $1 \leq c < d$, there exists a language
computable in time $n^d$ with $a$ bits of advice but not in time $n^c$
with $a$ bits of advice. A semantic ... more >>>


TR04-002 | 8th January 2004
Troy Lee, Dieter van Melkebeek, Harry Buhrman

Language Compression and Pseudorandom Generators

The language compression problem asks for succinct descriptions of
the strings in a language A such that the strings can be efficiently
recovered from their description when given a membership oracle for
A. We study randomized and nondeterministic decompression schemes
and investigate how close we can get to the information ... more >>>


TR02-028 | 15th May 2002
Eric Allender, Harry Buhrman, Michal Koucky, Detlef Ronneburger, Dieter van Melkebeek

Power from Random Strings

Revisions: 1

We consider sets of strings with high Kolmogorov complexity, mainly
in resource-bounded settings but also in the traditional
recursion-theoretic sense. We present efficient reductions, showing
that these sets are hard and complete for various complexity classes.

In particular, in addition to the usual Kolmogorov complexity measure
K, ... more >>>


TR00-028 | 17th April 2000
Lance Fortnow, Dieter van Melkebeek

Time-Space Tradeoffs for Nondeterministic Computation

We show new tradeoffs for satisfiability and nondeterministic
linear time. Satisfiability cannot be solved on general purpose
random-access Turing machines in time $n^{1.618}$ and space
$n^{o(1)}$. This improves recent results of Lipton and Viglas and
Fortnow.

more >>>

TR98-075 | 9th December 1998
Adam Klivans, Dieter van Melkebeek

Graph Nonisomorphism has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses.

We establish hardness versus randomness trade-offs for a
broad class of randomized procedures. In particular, we create efficient
nondeterministic simulations of bounded round Arthur-Merlin games using
a language in exponential time that cannot be decided by polynomial
size oracle circuits with access to satisfiability. We show that every
language with ... more >>>


TR98-058 | 2nd August 1998
H. Buhrman, Dieter van Melkebeek, K.W. Regan, Martin Strauss, D. Sivakumar

A Generalization of Resource-Bounded Measure, With Application to the BPP vs. EXP Problem

We introduce "resource-bounded betting games", and propose
a generalization of Lutz's resource-bounded measure in which the choice
of next string to bet on is fully adaptive. Lutz's martingales are
equivalent to betting games constrained to bet on strings in lexicographic
order. We show that if strong pseudo-random number generators exist,
more >>>




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