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Electronic Colloquium on Computational Complexity

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Reports tagged with branching program:
TR95-001 | 1st January 1995
Amos Beimel, Anna Gal, Michael S. Paterson

Lower Bounds for Monotone Span Programs

The model of span programs is a linear algebraic model of
computation. Lower bounds for span programs imply lower bounds for
contact schemes, symmetric branching programs and for formula size.
Monotone span programs correspond also to linear secret-sharing schemes.
We present a new technique for proving lower bounds for ... more >>>

TR97-019 | 5th May 1997
Martin Sauerhoff

A Lower Bound for Randomized Read-k-Times Branching Programs

In this paper, we are concerned with randomized OBDDs and randomized
read-k-times branching programs. We present an example of a Boolean
function which has polynomial size randomized OBDDs with small,
one-sided error, but only non-deterministic read-once branching
programs of exponential size. Furthermore, we discuss a lower bound
technique for randomized ... more >>>

TR98-077 | 19th December 1998
Miklos Ajtai

Determinism versus Non-Determinism for Linear Time RAMs with Memory Restrictions

Revisions: 1

Our computational model is a random access machine with $n$
read only input registers each containing $ c \log n$ bits of
information and a read and write memory. We measure the time by the
number of accesses to the input registers. We show that for all $k$
there is ... more >>>

TR99-026 | 7th July 1999
Miklos Ajtai

A Non-linear Time Lower Bound for Boolean Branching Programs

We prove that for all positive integer $k$ and for all
sufficiently small $\epsilon >0$ if $n$ is sufficiently large
then there is no Boolean (or $2$-way) branching program of size
less than $2^{\epsilon n}$ which for all inputs
$X\subseteq \lbrace 0,1,...,n-1\rbrace $ computes in time $kn$
the parity of ... more >>>

TR00-006 | 26th January 2000
E.A. Okol'nishnikiva

On operations of geometrical projection and monotone extension

Some operations over Boolean functions are considered. It is shown that
the operation of the geometrical projection and the operation of the
monotone extension can increase the complexity of Boolean functions for
formulas in each finite basis, for switching networks, for branching
programs, and read-$k$-times ... more >>>

TR01-017 | 14th February 2001
Petr Savicky, Detlef Sieling

A Hierarchy Result for Read-Once Branching Programs with Restricted Parity Nondeterminism

Restricted branching programs are considered in complexity theory in
order to study the space complexity of sequential computations and
in applications as a data structure for Boolean functions. In this
paper (\oplus,k)-branching programs and (\vee,k)-branching
programs are considered, i.e., branching programs starting with a
... more >>>

TR01-037 | 21st February 2001
Rustam Mubarakzjanov

Bounded-Width Probabilistic OBDDs and Read-Once Branching Programs are Incomparable

Restricted branching programs are considered by the investigation
of relationships between complexity classes of Boolean functions.
Read-once ordered branching programs (or OBDDs) form the most restricted class
of this computation model.
Since the problem of proving exponential lower bounds on the complexity
for general probabilistic OBDDs is open so ... more >>>

TR01-039 | 18th May 2001
Stasys Jukna, Stanislav Zak

On Uncertainty versus Size in Branching Programs

Revisions: 1

We propose an information-theoretic approach to proving lower
bounds on the size of branching programs. The argument is based on
Kraft-McMillan type inequalities for the average amount of
uncertainty about (or entropy of) a given input during the various
stages of computation. The uncertainty is measured by the average
more >>>

TR01-048 | 3rd June 2001
Jui-Lin Lee

Branching program, commutator, and icosahedron, part I

In this paper we give a direct proof of $N_0=N_0^\prime$, i.e., the equivalence of
uniform $NC^1$ based on different recursion principles: one is OR-AND complete
binary tree (in depth $\log n$) and the other is the recursion on notation with value
bounded in $[0,k]$ and $|x|(=n)$ many ... more >>>

TR12-041 | 17th April 2012
Stasys Jukna

Limitations of Incremental Dynamic Programs

Revisions: 1

We consider so-called ``incremental'' dynamic programming (DP) algorithms, and are interested in the number of subproblems produced by them. The standard DP algorithm for the n-dimensional Knapsack problem is incremental, and produces nK subproblems, where K is the capacity of the knapsack. We show that any incremental algorithm for this ... more >>>

TR13-119 | 2nd September 2013
Emanuele Viola

Challenges in computational lower bounds

We draw two incomplete, biased maps of challenges in
computational complexity lower bounds. Our aim is to put
these challenges in perspective, and to present some
connections which do not seem widely known.

more >>>

TR14-105 | 9th August 2014
Craig Gentry

Noncommutative Determinant is Hard: A Simple Proof Using an Extension of Barrington’s Theorem

Comments: 1

We show that, for many noncommutative algebras A, the hardness of computing the determinant of matrices over A follows almost immediately from Barrington’s Theorem. Barrington showed how to express a NC1 circuit as a product program over any non-solvable group. We construct a simple matrix directly from Barrington’s product program ... more >>>

TR17-020 | 12th February 2017
Ran Raz

A Time-Space Lower Bound for a Large Class of Learning Problems

We prove a general time-space lower bound that applies for a large class of learning problems and shows that for every problem in that class, any learning algorithm requires either a memory of quadratic size or an exponential number of samples.

Our result is stated in terms of the norm ... more >>>

TR17-121 | 31st July 2017
Sumegha Garg, Ran Raz, Avishay Tal

Extractor-Based Time-Space Lower Bounds for Learning

Revisions: 1

A matrix $M: A \times X \rightarrow \{-1,1\}$ corresponds to the following learning problem: An unknown element $x \in X$ is chosen uniformly at random. A learner tries to learn $x$ from a stream of samples, $(a_1, b_1), (a_2, b_2) \ldots$, where for every $i$, $a_i \in A$ is chosen ... more >>>

TR18-015 | 25th January 2018
Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett

Pseudorandom Generators from Polarizing Random Walks

Revisions: 1 , Comments: 1

We propose a new framework for constructing pseudorandom generators for $n$-variate Boolean functions. It is based on two new notions. First, we introduce fractional pseudorandom generators, which are pseudorandom distributions taking values in $[-1,1]^n$. Next, we use a fractional pseudorandom generator as steps of a random walk in $[-1,1]^n$ that ... more >>>

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