All reports by Author Dieter van Melkebeek:

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TR23-029
| 18th March 2023
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Nicollas Sdroievski, Dieter van Melkebeek#### Instance-Wise Hardness versus Randomness Tradeoffs for Arthur-Merlin Protocols

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TR22-158
| 18th November 2022
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Ivan Hu, Andrew Morgan, Dieter van Melkebeek#### Query Complexity of Inversion Minimization on Trees

Revisions: 1

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TR22-115
| 17th August 2022
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Dieter van Melkebeek, Andrew Morgan#### Polynomial Identity Testing via Evaluation of Rational Functions

Revisions: 2

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TR17-158
| 23rd October 2017
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Eric Allender, Joshua Grochow, Dieter van Melkebeek, Cris Moore, Andrew Morgan#### Minimum Circuit Size, Graph Isomorphism, and Related Problems

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TR17-052
| 19th March 2017
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Dieter van Melkebeek, Gautam Prakriya#### Derandomizing Isolation in Space-Bounded Settings

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TR12-080
| 18th June 2012
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Baris Aydinlioglu, Dieter van Melkebeek#### Nondeterministic Circuit Lower Bounds from Mildly Derandomizing Arthur-Merlin Games

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TR11-158
| 25th November 2011
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Matthew Anderson, Dieter van Melkebeek, Nicole Schweikardt, Luc Segoufin#### Locality from Circuit Lower Bounds

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TR10-188
| 8th December 2010
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Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich#### Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae

Revisions: 1

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TR10-174
| 12th November 2010
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Scott Aaronson, Baris Aydinlioglu, Harry Buhrman, John Hitchcock, Dieter van Melkebeek#### A note on exponential circuit lower bounds from derandomizing Arthur-Merlin games

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TR10-147
| 22nd September 2010
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Dieter van Melkebeek, Thomas Watson#### Time-Space Efficient Simulations of Quantum Computations

Revisions: 1

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TR10-129
| 16th August 2010
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Jeff Kinne, Dieter van Melkebeek, Ronen Shaltiel#### Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds

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TR10-105
| 29th June 2010
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Scott Aaronson, Dieter van Melkebeek#### A note on circuit lower bounds from derandomization

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TR10-038
| 10th March 2010
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Dieter van Melkebeek, Holger Dell#### Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses

Revisions: 1

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TR08-017
| 16th December 2007
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Thomas Watson, Dieter van Melkebeek#### A Quantum Time-Space Lower Bound for the Counting Hierarchy

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TR07-134
| 14th December 2007
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Jeff Kinne, Dieter van Melkebeek#### Space Hierarchy Results for Randomized and Other Semantic Models

Revisions: 1

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TR07-099
| 30th September 2007
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Dieter van Melkebeek#### A Survey of Lower Bounds for Satisfiability and Related Problems

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TR05-111
| 3rd October 2005
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Dieter van Melkebeek, Konstantin Pervyshev#### A Generic Time Hierarchy for Semantic Models With One Bit of Advice

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TR04-002
| 8th January 2004
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Troy Lee, Dieter van Melkebeek, Harry Buhrman#### Language Compression and Pseudorandom Generators

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

Revisions: 1
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Comments: 1

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TR00-028
| 17th April 2000
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Lance Fortnow, Dieter van Melkebeek#### Time-Space Tradeoffs for Nondeterministic Computation

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TR98-075
| 9th December 1998
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Adam Klivans, Dieter van Melkebeek#### Graph Nonisomorphism has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses.

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TR98-058
| 2nd August 1998
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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

Nicollas Sdroievski, Dieter van Melkebeek

A fundamental question in computational complexity asks whether probabilistic polynomial-time algorithms can be simulated deterministically with a small overhead in time (the BPP vs. P problem). A corresponding question in the realm of interactive proofs asks whether Arthur-Merlin protocols can be simulated nondeterministically with a small overhead in time (the ... more >>>

Ivan Hu, Andrew Morgan, Dieter van Melkebeek

We consider the following computational problem: Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the well-known problem of counting inversions in arrays originated in mathematical psychology. It ... more >>>

Dieter van Melkebeek, Andrew Morgan

We introduce a hitting set generator for Polynomial Identity Testing

based on evaluations of low-degree univariate rational functions at

abscissas associated with the variables. Despite the univariate

nature, we establish an equivalence up to rescaling with a generator

introduced by Shpilka and Volkovich, which has a similar structure but

uses ...
more >>>

Eric Allender, Joshua Grochow, Dieter van Melkebeek, Cris Moore, Andrew Morgan

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 >>>

Dieter van Melkebeek, Gautam Prakriya

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 >>>

Baris Aydinlioglu, Dieter van Melkebeek

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 >>>

Matthew Anderson, Dieter van Melkebeek, Nicole Schweikardt, Luc Segoufin

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 >>>

Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich

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 >>>

Scott Aaronson, Baris Aydinlioglu, Harry Buhrman, John Hitchcock, Dieter van Melkebeek

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 >>>

Dieter van Melkebeek, Thomas Watson

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 >>>

Jeff Kinne, Dieter van Melkebeek, Ronen Shaltiel

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 >>>

Scott Aaronson, Dieter van Melkebeek

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 >>>Dieter van Melkebeek, Holger Dell

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 >>>

Thomas Watson, Dieter van Melkebeek

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 >>>

Jeff Kinne, Dieter van Melkebeek

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 >>>

Dieter van Melkebeek

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 >>>

Dieter van Melkebeek, Konstantin Pervyshev

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 ...
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Troy Lee, Dieter van Melkebeek, Harry Buhrman

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 >>>

Eric Allender, Harry Buhrman, Michal Koucky, Detlef Ronneburger, Dieter van Melkebeek

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 >>>

Lance Fortnow, Dieter van Melkebeek

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.

Adam Klivans, Dieter van Melkebeek

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 >>>

H. Buhrman, Dieter van Melkebeek, K.W. Regan, Martin Strauss, D. Sivakumar

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 >>>