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Electronic Colloquium on Computational Complexity

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Reports tagged with read-once branching programs:
TR97-030 | 25th August 1997
Martin Sauerhoff

On Nondeterminism versus Randomness for Read-Once Branching Programs

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 ... more >>>

TR00-048 | 3rd July 2000
Beate Bollig

Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication

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
more >>>

TR01-066 | 28th September 2001
Pavol Duris, Juraj Hromkovic, Stasys Jukna, Martin Sauerhoff, Georg Schnitger

On Multipartition Communication Complexity

We study k-partition communication protocols, an extension
of the standard two-party best-partition model to k input partitions.
The main results are as follows.

1. A strong explicit hierarchy on the degree of
non-obliviousness is established by proving that,
using k+1 partitions instead of k may decrease
the communication complexity from ... more >>>

TR07-110 | 24th October 2007
Beate Bollig

The Optimal Read-Once Branching Program Complexity for the Direct Storage Access Function

Branching programs are computation models
measuring the space of (Turing machine) computations.
Read-once branching programs (BP1s) are the
most general model where each graph-theoretical path is the computation
path for some input. Exponential lower bounds on the size of read-once
branching programs are known since a long time. Nevertheless, there ... more >>>

TR10-088 | 17th May 2010
Jiri Sima, Stanislav Zak

A Polynomial Time Construction of a Hitting Set for Read-Once Branching Programs of Width 3

Revisions: 2 , Comments: 3

The relationship between deterministic and probabilistic computations is one of the central issues in complexity theory. This problem can be tackled by constructing polynomial time hitting set generators which, however, belongs to the hardest problems in computer science even for severely restricted computational models. In our work, we consider read-once ... more >>>

TR10-176 | 15th November 2010
Parikshit Gopalan, Raghu Meka, Omer Reingold, David Zuckerman

Pseudorandom Generators for Combinatorial Shapes

Revisions: 1

We construct pseudorandom generators for combinatorial shapes, which substantially generalize combinatorial rectangles, small-bias spaces, 0/1 halfspaces, and 0/1 modular sums. A function $f:[m]^n \rightarrow \{0,1\}^n$ is an $(m,n)$-combinatorial shape if there exist sets $A_1,\ldots,A_n \subseteq [m]$ and a symmetric function $h:\{0,1\}^n \rightarrow \{0,1\}$ such that $f(x_1,\ldots,x_n) = h(1_{A_1} (x_1),\ldots,1_{A_n}(x_n))$. Our ... more >>>

TR13-132 | 23rd September 2013
Michael Forbes, Ramprasad Saptharishi, Amir Shpilka

Pseudorandomness for Multilinear Read-Once Algebraic Branching Programs, in any Order

We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in n^(lg^2 n) time. Further, our algorithm is oblivious to the order of the variables. This is the first sub-exponential time algorithm for this model. Furthermore, our result has no known analogue in the ... more >>>

TR17-161 | 30th October 2017
Mark Braverman, Gil Cohen, Sumegha Garg

Hitting Sets with Near-Optimal Error for Read-Once Branching Programs

Revisions: 1

Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$, or to construct improved hitting sets, as ... more >>>

TR18-063 | 5th April 2018
William Hoza, David Zuckerman

Simple Optimal Hitting Sets for Small-Success $\mathbf{RL}$

Revisions: 1

We give a simple explicit hitting set generator for read-once branching programs of width $w$ and length $r$ with known variable order. Our generator has seed length $O\left(\frac{\log(wr) \log r}{\max\{1, \log \log w - \log \log r\}} + \log(1/\varepsilon)\right)$. This seed length improves on recent work by Braverman, Cohen, and ... more >>>

TR18-147 | 19th August 2018
Michael Forbes, Zander Kelley

Pseudorandom Generators for Read-Once Branching Programs, in any Order

A central question in derandomization is whether randomized logspace (RL) equals deterministic logspace (L). To show that RL=L, it suffices to construct explicit pseudorandom generators (PRGs) that fool polynomial-size read-once (oblivious) branching programs (roBPs). Starting with the work of Nisan, pseudorandom generators with seed-length $O(\log^2 n)$ were constructed. Unfortunately, ... more >>>

TR21-083 | 21st June 2021
Mark Braverman, Sumegha Garg, Or Zamir

Tight Space Complexity of the Coin Problem

In the coin problem we are asked to distinguish, with probability at least $2/3$, between $n$ $i.i.d.$ coins which are heads with probability $\frac{1}{2}+\beta$ from ones which are heads with probability $\frac{1}{2}-\beta$. We are interested in the space complexity of the coin problem, corresponding to the width of a read-once ... more >>>

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