Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > TIME-SPACE TRADEOFFS:
TR95-010 | 16th February 1995
Pavel Pudlak, Jiri Sgall

#### An Upper Bound for a Communication Game Related to Time-Space Tradeoffs

We prove an unexpected upper bound on a communication game proposed
by Jeff Edmonds and Russell Impagliazzo as an approach for
proving lower bounds for time-space tradeoffs for branching programs.
Our result is based on a generalization of a construction of Erdos,
Frankl and Rodl of a large 3-hypergraph ... more >>>

TR98-053 | 30th August 1998
Paul Beame, Michael Saks, Jayram S. Thathachar

#### Time-Space Tradeoffs for Branching Programs

We obtain the first non-trivial time-space tradeoff lower bound for
functions f:{0,1}^n ->{0,1} on general branching programs by exhibiting a
Boolean function f that requires exponential size to be computed by any
branching program of length cn, for some constant c>1. We also give the first
separation result between the ... more >>>

TR00-025 | 20th May 2000
Paul Beame, Michael Saks, Xiaodong Sun, Erik Vee

#### Super-linear time-space tradeoff lower bounds for randomized computation

We prove the first time-space lower bound tradeoffs for randomized
computation of decision problems. The bounds hold even in the
case that the computation is allowed to have arbitrary probability
of error on a small fraction of inputs. Our techniques are an
extension of those used by Ajtai in his ... 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 >>>

TR01-041 | 23rd May 2001
Eric Allender, Michal Koucky, Detlef Ronneburger, Sambuddha Roy, V. Vinay

#### Time-Space Tradeoffs in the Counting Hierarchy

We extend the lower bound techniques of [Fortnow], to the
unbounded-error probabilistic model. A key step in the argument
is a generalization of Nepomnjascii's theorem from the Boolean
setting to the arithmetic setting. This generalization is made
possible, due to the recent discovery of logspace-uniform TC^0
more >>>

TR02-038 | 5th June 2002
Rahul Santhanam

Revisions: 1

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 ... more >>>

TR07-036 | 6th April 2007
Ryan Williams

#### Time-Space Tradeoffs for Counting NP Solutions Modulo Integers

We prove the first time-space tradeoffs for counting the number of solutions to an NP problem modulo small integers, and also improve upon the known time-space tradeoffs for Sat. Let m be a positive integer, and define MODm-Sat to be the problem of determining if a given Boolean formula has ... 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 >>>

TR09-002 | 23rd November 2008
Eli Ben-Sasson, Jakob Nordström

#### Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution

A number of works have looked at the relationship between length and space of resolution proofs. A notorious question has been whether the existence of a short proof implies the existence of a proof that can be verified using limited space.

In this paper we resolve the question by answering ... more >>>

TR10-104 | 29th June 2010

#### Making RAMs Oblivious Requires Superlogarithmic Overhead

We prove a time-space tradeoff lower bound of $T = \Omega\left(n\log(\frac{n}{S}) \log \log(\frac{n}{S})\right)$ for
randomized oblivious branching programs to compute $1GAP$, also
known as the pointer jumping problem, a problem for which there is a
simple deterministic time $n$ and space $O(\log n)$ RAM (random
access machine) algorithm.

In ... more >>>

TR13-127 | 15th September 2013
Paul Beame, Raphael Clifford, Widad Machmouchi

#### Element Distinctness, Frequency Moments, and Sliding Windows

We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. In particular, we develop a randomized algorithm for the element distinctness problem whose time $T$ and space $S$ ... more >>>

TR17-120 | 31st July 2017
Paul Beame, Shayan Oveis Gharan, Xin Yang

#### Time-Space Tradeoffs for Learning from Small Test Spaces: Learning Low Degree Polynomial Functions

Revisions: 1

We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space of inputs, a class of learning problems that is not handled by prior ... more >>>

ISSN 1433-8092 | Imprint