67,741 research outputs found
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)
Efficient Analysis of Complex Diagrams using Constraint-Based Parsing
This paper describes substantial advances in the analysis (parsing) of
diagrams using constraint grammars. The addition of set types to the grammar
and spatial indexing of the data make it possible to efficiently parse real
diagrams of substantial complexity. The system is probably the first to
demonstrate efficient diagram parsing using grammars that easily be retargeted
to other domains. The work assumes that the diagrams are available as a flat
collection of graphics primitives: lines, polygons, circles, Bezier curves and
text. This is appropriate for future electronic documents or for vectorized
diagrams converted from scanned images. The classes of diagrams that we have
analyzed include x,y data graphs and genetic diagrams drawn from the biological
literature, as well as finite state automata diagrams (states and arcs). As an
example, parsing a four-part data graph composed of 133 primitives required 35
sec using Macintosh Common Lisp on a Macintosh Quadra 700.Comment: 9 pages, Postscript, no fonts, compressed, uuencoded. Composed in
MSWord 5.1a for the Mac. To appear in ICDAR '95. Other versions at
ftp://ftp.ccs.neu.edu/pub/people/futrell
Error-tolerant Finite State Recognition with Applications to Morphological Analysis and Spelling Correction
Error-tolerant recognition enables the recognition of strings that deviate
mildly from any string in the regular set recognized by the underlying finite
state recognizer. Such recognition has applications in error-tolerant
morphological processing, spelling correction, and approximate string matching
in information retrieval. After a description of the concepts and algorithms
involved, we give examples from two applications: In the context of
morphological analysis, error-tolerant recognition allows misspelled input word
forms to be corrected, and morphologically analyzed concurrently. We present an
application of this to error-tolerant analysis of agglutinative morphology of
Turkish words. The algorithm can be applied to morphological analysis of any
language whose morphology is fully captured by a single (and possibly very
large) finite state transducer, regardless of the word formation processes and
morphographemic phenomena involved. In the context of spelling correction,
error-tolerant recognition can be used to enumerate correct candidate forms
from a given misspelled string within a certain edit distance. Again, it can be
applied to any language with a word list comprising all inflected forms, or
whose morphology is fully described by a finite state transducer. We present
experimental results for spelling correction for a number of languages. These
results indicate that such recognition works very efficiently for candidate
generation in spelling correction for many European languages such as English,
Dutch, French, German, Italian (and others) with very large word lists of root
and inflected forms (some containing well over 200,000 forms), generating all
candidate solutions within 10 to 45 milliseconds (with edit distance 1) on a
SparcStation 10/41. For spelling correction in Turkish, error-tolerantComment: Replaces 9504031. gzipped, uuencoded postscript file. To appear in
Computational Linguistics Volume 22 No:1, 1996, Also available as
ftp://ftp.cs.bilkent.edu.tr/pub/ko/clpaper9512.ps.
Tabular Parsing
This is a tutorial on tabular parsing, on the basis of tabulation of
nondeterministic push-down automata. Discussed are Earley's algorithm, the
Cocke-Kasami-Younger algorithm, tabular LR parsing, the construction of parse
trees, and further issues.Comment: 21 pages, 14 figure
Efficient Algorithms for Morphisms over Omega-Regular Languages
Morphisms to finite semigroups can be used for recognizing omega-regular
languages. The so-called strongly recognizing morphisms can be seen as a
deterministic computation model which provides minimal objects (known as the
syntactic morphism) and a trivial complementation procedure. We give a
quadratic-time algorithm for computing the syntactic morphism from any given
strongly recognizing morphism, thereby showing that minimization is easy as
well. In addition, we give algorithms for efficiently solving various decision
problems for weakly recognizing morphisms. Weakly recognizing morphism are
often smaller than their strongly recognizing counterparts. Finally, we
describe the language operations needed for converting formulas in monadic
second-order logic (MSO) into strongly recognizing morphisms, and we give some
experimental results.Comment: Full version of a paper accepted to FSTTCS 201
Streaming algorithms for language recognition problems
We study the complexity of the following problems in the streaming model.
Membership testing for \DLIN We show that every language in \DLIN\ can be
recognised by a randomized one-pass space algorithm with inverse
polynomial one-sided error, and by a deterministic p-pass space
algorithm. We show that these algorithms are optimal.
Membership testing for \LL For languages generated by \LL grammars
with a bound of on the number of nonterminals at any stage in the left-most
derivation, we show that membership can be tested by a randomized one-pass
space algorithm with inverse polynomial (in ) one-sided error.
Membership testing for \DCFL We show that randomized algorithms as efficient
as the ones described above for \DLIN\ and \LL(k) (which are subclasses of
\DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass
of \DCFL) for which any randomized p-pass algorithm with error bounded by
must use space.
Degree sequence problem We study the problem of determining, given a sequence
and a graph , whether the degree sequence of is
precisely . We give a randomized one-pass space
algorithm with inverse polynomial one-sided error probability. We show that our
algorithms are optimal.
Our randomized algorithms are based on the recent work of Magniez et al.
\cite{MMN09}; our lower bounds are obtained by considering related
communication complexity problems
LEGaTO: first steps towards energy-efficient toolset for heterogeneous computing
LEGaTO is a three-year EU H2020 project which started in December 2017. The LEGaTO project will leverage task-based programming models to provide a software ecosystem for Made-in-Europe heterogeneous hardware composed of CPUs, GPUs, FPGAs and dataflow engines. The aim is to attain one order of magnitude energy savings from the edge to the converged cloud/HPC.Peer ReviewedPostprint (author's final draft
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