Stephen A. Bloch, Jonathan F. Buss, Judy Goldsmith

We define the sharply bounded hierarchy, SBHQL, a hierarchy of

classes within P, using quasilinear-time computation and

quantification over values of length log n. It generalizes the

limited nondeterminism hierarchy introduced by Buss and Goldsmith,

while retaining the invariance properties. The new hierarchy has

several alternative characterizations.

We define ... more >>>

Pavol Duris, Juraj Hromkovic, Jose' D. P. Rolim, Georg Schnitger

The study of the computational power of randomized

computations is one of the central tasks of complexity theory. The

main goal of this paper is the comparison of the power of Las Vegas

computation and deterministic respectively nondeterministic

computation. We investigate the power of Las Vegas computation for ...
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Martin Sauerhoff

Randomized branching programs are a probabilistic model of computation

defined in analogy to the well-known probabilistic Turing machines.

In this paper, we present complexity theoretic results for randomized

read-once branching programs.

Our main result shows that nondeterminism can be more powerful than

randomness for read-once branching programs. We present a ...
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Martin Sauerhoff

We extend the tools for proving lower bounds for randomized branching

programs by presenting a new technique for the read-once case which is

applicable to a large class of functions. This technique fills the gap

between simple methods only applicable for OBDDs and the well-known

"rectangle technique" of Borodin, Razborov ...
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Juraj Hromkovic, Georg Schnitger

The investigation of the computational power of randomized

computations is one of the central tasks of current complexity and

algorithm theory. This paper continues in the comparison of the computational

power of LasVegas computations with the computational power of deterministic

and nondeterministic ones. While for one-way ...
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Beate Bollig

Branching programs are a well established computation model for

Boolean functions, especially read-once branching programs have

been studied intensively.

In this paper the expressive power of nondeterministic read-once

branching programs, i.e., the class of functions

representable in polynomial size, is investigated.

For that reason two restricted models of nondeterministic read-once

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Martin Sauerhoff

One of the great challenges of complexity theory is the problem of

analyzing the dependence of the complexity of Boolean functions on the

resources nondeterminism and randomness. So far, this problem could be

solved only for very few models of computation. For so-called

partitioned binary decision diagrams, which are a ...
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Martin Sauerhoff

This paper deals with the number of monochromatic combinatorial

rectangles required to approximate a Boolean function on a constant

fraction of all inputs, where each rectangle may be defined with

respect to its own partition of the input variables. The main result

of the paper is that the number of ...
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Juraj Hromkovic, Juhani Karhumaki, Hartmut Klauck, Georg Schnitger, Sebastian Seibert

While deterministic finite automata seem to be well understood, surprisingly

many important problems

concerning nondeterministic finite automata (nfa's) remain open.

One such problem area is the study of different measures of nondeterminism in

finite automata and the

estimation of the sizes of minimal nondeterministic finite automata. In this

paper the ...
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Philipp Woelfel

We present a new lower bound technique for two types of restricted

Branching Programs (BPs), namely for read-once BPs (BP1s) with

restricted amount of nondeterminism and for (1,+k)-BPs. For this

technique, we introduce the notion of (strictly) k-wise l-mixed

Boolean functions, which generalizes the concept of l-mixedness ...
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Beate Bollig

Branching programs are a well-established computation

model for boolean functions, especially read-once

branching programs (BP1s) have been studied intensively.

A very simple function $f$ in $n^2$ variables is

exhibited such that both the function $f$ and its negation

$\neg f$ can be computed by $\Sigma^3_p$-circuits,

the ...
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Rahul Santhanam

We consider uniform assumptions for derandomization. We provide

intuitive evidence that BPP can be simulated non-trivially in

deterministic time by showing that (1) P \not \subseteq i.o.i.PLOYLOGSPACE

implies BPP \subseteq SUBEXP (2) P \not \subseteq SUBPSPACE implies BPP

= P. These results extend and complement earlier work of ...
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Emanuele Viola, Avi Wigderson

In this paper we study the one-way multi-party communication model,

in which every party speaks exactly once in its turn. For every

fixed $k$, we prove a tight lower bound of

$\Omega{n^{1/(k-1)}}$ on the probabilistic communication

complexity of pointer jumping in a $k$-layered tree, where the

pointers of the $i$-th ...
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Nathaniel Bryans, Ehsan Chiniforooshan, David Doty, Lila Kari, Shinnosuke Seki

We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Designing tile systems that assemble shapes, due to the algorithmic richness of the aTAM, is a form of sophisticated "molecular programming". Of particular practical importance ... more >>>

Marco Carmosino, Jiawei Gao, Russell Impagliazzo, Ivan Mikhailin, Ramamohan Paturi, Stefan Schneider

We introduce the Nondeterministic Strong Exponential Time Hypothesis

(NSETH) as a natural extension of the Strong Exponential Time

Hypothesis (SETH). We show that both refuting and proving

NSETH would have interesting consequences.

In particular we show that disproving NSETH would ...
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Juraj Hromkovic

We call any consistent and sufficiently powerful formal theory that enables to algorithmically in polynomial time verify whether a text is a proof \textbf{efficiently verifiable mathematics} (ev-mathematics). We study the question whether nondeterminism is more powerful than determinism for polynomial time computations in the framework of ev-mathematics. Our main results ... more >>>

Marshall Ball, Dana Dachman-Soled, Julian Loss

We present the first truly explicit constructions of \emph{non-malleable codes} against tampering by bounded polynomial size circuits. These objects imply unproven circuit lower bounds and our construction is secure provided E requires exponential size nondeterministic circuits, an assumption from the derandomization literature.

Prior works on NMC ...
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