254 research outputs found
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
If the Current Clique Algorithms are Optimal, so is Valiant's Parser
The CFG recognition problem is: given a context-free grammar
and a string of length , decide if can be obtained from
. This is the most basic parsing question and is a core computer
science problem. Valiant's parser from 1975 solves the problem in
time, where is the matrix multiplication
exponent. Dozens of parsing algorithms have been proposed over the years, yet
Valiant's upper bound remains unbeaten. The best combinatorial algorithms have
mildly subcubic complexity.
Lee (JACM'01) provided evidence that fast matrix multiplication is needed for
CFG parsing, and that very efficient and practical algorithms might be hard or
even impossible to obtain. Lee showed that any algorithm for a more general
parsing problem with running time can
be converted into a surprising subcubic algorithm for Boolean Matrix
Multiplication. Unfortunately, Lee's hardness result required that the grammar
size be . Nothing was known for the more relevant
case of constant size grammars.
In this work, we prove that any improvement on Valiant's algorithm, even for
constant size grammars, either in terms of runtime or by avoiding the
inefficiencies of fast matrix multiplication, would imply a breakthrough
algorithm for the -Clique problem: given a graph on nodes, decide if
there are that form a clique.
Besides classifying the complexity of a fundamental problem, our reduction
has led us to similar lower bounds for more modern and well-studied cubic time
problems for which faster algorithms are highly desirable in practice: RNA
Folding, a central problem in computational biology, and Dyck Language Edit
Distance, answering an open question of Saha (FOCS'14)
On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic are investigated for this class of monoids. The first main result shows that for any consistent combination of these properties and their negations, there is a homogeneous monoid with exactly this combination of properties. We then introduce the new concept of abstract Rees-commensurability (an analogue of the notion of abstract commensurability for groups) in order to extend this result to show that the same statement holds even if one restricts attention to the class of n-ary homogeneous monoids (where every side of every relation has fixed length n). We then introduce a new encoding technique that allows us to extend the result partially to the class of n-ary multihomogenous monoids
On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic are investigated for this class of monoids. The first main result shows that for any consistent combination of these properties and their negations, there is a homogeneous monoid with exactly this combination of properties. We then introduce the new concept of abstract Rees-commensurability (an analogue of the notion of abstract commensurability for groups) in order to extend this result to show that the same statement holds even if one restricts attention to the class of n-ary homogeneous monoids (where every side of every relation has fixed length n). We then introduce a new encoding technique that allows us to extend the result partially to the class of n-ary multihomogenous monoids
Corporate influence and the academic computer science discipline. [4: CMU]
Prosopographical work on the four major centers for computer
research in the United States has now been conducted, resulting in big
questions about the independence of, so called, computer science
- …