4,740 research outputs found
Some Lower Bound Results for Set-Multilinear Arithmetic Computations
In this paper, we study the structure of set-multilinear arithmetic circuits
and set-multilinear branching programs with the aim of showing lower bound
results. We define some natural restrictions of these models for which we are
able to show lower bound results. Some of our results extend existing lower
bounds, while others are new and raise open questions. More specifically, our
main results are the following:
(1) We observe that set-multilinear arithmetic circuits can be transformed
into shallow set-multilinear circuits efficiently, similar to depth reduction
results of [VSBR83,RY08] for more general commutative circuits. As a
consequence, we note that polynomial size set-multilinear circuits have
quasi-polynomial size set-multilinear branching programs. We show that
\emph{narrow} set-multilinear ABPs (with a restricted number of set types)
computing the Permanent polynomial require
size. A similar result for general set-multilinear ABPs appears difficult as it
would imply that the Permanent requires superpolynomial size set-multilinear
circuits. It would also imply that the noncommutative Permanent requires
superpolynomial size noncommutative arithmetic circuits.
(2) Indeed, we also show that set-multilinear branching programs are
exponentially more powerful than \emph{interval} multilinear circuits (where
the index sets for each gate is restricted to be an interval w.r.t.\ some
ordering), assuming the sum-of-squares conjecture. This further underlines the
power of set-multilinear branching programs.
(3) Finally, we consider set-multilinear circuits with restrictions on the
number of proof trees of monomials computed by it, and prove exponential lower
bounds results. This raises some new lower bound questions
Detecting and resolving spatial ambiguity in text using named entity extraction and self learning fuzzy logic techniques
Information extraction identifies useful and relevant text in a document and
converts unstructured text into a form that can be loaded into a database
table. Named entity extraction is a main task in the process of information
extraction and is a classification problem in which words are assigned to one
or more semantic classes or to a default non-entity class. A word which can
belong to one or more classes and which has a level of uncertainty in it can be
best handled by a self learning Fuzzy Logic Technique. This paper proposes a
method for detecting the presence of spatial uncertainty in the text and
dealing with spatial ambiguity using named entity extraction techniques coupled
with self learning fuzzy logic techniquesComment: National Conference on Recent Trends in Data Mining and Distributed
Systems September 201
A Fuzzy Logic based Method for Efficient Retrieval of Vague and Uncertain Spatial Expressions in Text Exploiting the Granulation of the Spatial Event Queries
The arrangement of things in n-dimensional space is specified as Spatial.
Spatial data consists of values that denote the location and shape of objects
and areas on the earths surface. Spatial information includes facts such as
location of features, the relationship of geographic features and measurements
of geographic features. The spatial cognition is a primal area of study in
various other fields such as Robotics, Psychology, Geosciences, Geography,
Political Sciences, Geographic Economy, Environmental, Mining and Petroleum
Engineering, Natural Resources, Epidemiology, Demography etc., Any text
document which contains physical location specifications such as place names,
geographic coordinates, landmarks, country names etc., are supposed to contain
the spatial information. The spatial information may also be represented using
vague or fuzzy descriptions involving linguistic terms such as near to, far
from, to the east of, very close. Given a query involving events, the aim of
this ongoing research work is to extract the relevant information from multiple
text documents, resolve the uncertainty and vagueness and translate them in to
locations in a map. The input to the system would be a text Corpus and a
Spatial Query event. The output of the system is a map showing the most
possible, disambiguated location of the event queried. The author proposes
Fuzzy Logic Techniques for resolving the uncertainty in the spatial
expressions.Comment: National Conference on Future Computing,0975 8887,IJCA,February201
A Study on Application of Spatial Data Mining Techniques for Rural Progress
This paper focuses on the application of Spatial Data mining Techniques to
efficiently manage the challenges faced by peripheral rural areas in analyzing
and predicting market scenario and better manage their economy. Spatial data
mining is the task of unfolding the implicit knowledge hidden in the spatial
databases. The spatial Databases contain both spatial and non-spatial
attributes of the areas under study. Finding implicit regularities, rules or
patterns hidden in spatial databases is an important task, e.g. for
geo-marketing, traffic control or environmental studies. In this paper the
focus is on the effective use of Spatial Data Mining Techniques in the field of
Economic Geography constrained to the rural areasComment: International Conference on Innovative Computing, information and
communication technology ICICT09; souvenir pp no 6
Computational Model to Generate Case-Inflected Forms of Masculine Nouns for Word Search in Sanskrit E-Text
The problem of word search in Sanskrit is inseparable from complexities that
include those caused by euphonic conjunctions and case-inflections. The
case-inflectional forms of a noun normally number 24 owing to the fact that in
Sanskrit there are eight cases and three numbers-singular, dual and plural. The
traditional method of generating these inflectional forms is rather elaborate
owing to the fact that there are differences in the forms generated between
even very similar words and there are subtle nuances involved. Further, it
would be a cumbersome exercise to generate and search for 24 forms of a word
during a word search in a large text, using the currently available
case-inflectional form generators. This study presents a new approach to
generating case-inflectional forms that is simpler to compute. Further, an
optimized model that is sufficient for generating only those word forms that
are required in a word search and is more than 80% efficient compared to the
complete case-inflectional forms generator, is presented in this study for the
first time
An Ontology for Comprehensive Tutoring of Euphonic Conjunctions of Sanskrit Grammar
Euphonic conjunctions (sandhis) form a very important aspect of Sanskrit
morphology and phonology. The traditional and modern methods of studying about
euphonic conjunctions in Sanskrit follow different methodologies. The former
involves a rigorous study of the Paninian system embodied in Panini's
Ashtadhyayi, while the latter usually involves the study of a few important
sandhi rules with the use of examples. The former is not suitable for
beginners, and the latter, not sufficient to gain a comprehensive understanding
of the operation of sandhi rules. This is so since there are not only numerous
sandhi rules and exceptions, but also complex precedence rules involved. The
need for a new ontology for sandhi-tutoring was hence felt. This work presents
a comprehensive ontology designed to enable a student-user to learn in stages
all about euphonic conjunctions and the relevant aphorisms of Sanskrit grammar
and to test and evaluate the progress of the student-user. The ontology forms
the basis of a multimedia sandhi tutor that was given to different categories
of users including Sanskrit scholars for extensive and rigorous testing
A Binary Schema and Computational Algorithms to Process Vowel-based Euphonic Conjunctions for Word Searches
Comprehensively searching for words in Sanskrit E-text is a non-trivial
problem because words could change their forms in different contexts. One such
context is sandhi or euphonic conjunctions, which cause a word to change owing
to the presence of adjacent letters or words. The change wrought by these
possible conjunctions can be so significant in Sanskrit that a simple search
for the word in its given form alone can significantly reduce the success level
of the search. This work presents a representational schema that represents
letters in a binary format and reduces Paninian rules of euphonic conjunctions
to simple bit set-unset operations. The work presents an efficient algorithm to
process vowel-based sandhis using this schema. It further presents another
algorithm that uses the sandhi processor to generate the possible transformed
word forms of a given word to use in a comprehensive word search
Computational Algorithms Based on the Paninian System to Process Euphonic Conjunctions for Word Searches
Searching for words in Sanskrit E-text is a problem that is accompanied by
complexities introduced by features of Sanskrit such as euphonic conjunctions
or sandhis. A word could occur in an E-text in a transformed form owing to the
operation of rules of sandhi. Simple word search would not yield these
transformed forms of the word. Further, there is no search engine in the
literature that can comprehensively search for words in Sanskrit E-texts taking
euphonic conjunctions into account. This work presents an optimal binary
representational schema for letters of the Sanskrit alphabet along with
algorithms to efficiently process the sandhi rules of Sanskrit grammar. The
work further presents an algorithm that uses the sandhi processing algorithm to
perform a comprehensive word search on E-text
Randomized Polynomial Time Identity Testing for Noncommutative Circuits
In this paper we show that the black-box polynomial identity testing for
noncommutative polynomials
of degree and sparsity , can be done in randomized \poly(n,\log t,\log
D) time. As a consequence, if the black-box contains a circuit of size
computing which has at most
non-zero monomials, then the identity testing can be done by a randomized
algorithm with running time polynomial in and and . This makes
significant progress on a question that has been open for over ten years.
The earlier result by Bogdanov and Wee [BW05], using the classical
Amitsur-Levitski theorem, gives a randomized polynomial-time algorithm only for
circuits of polynomially bounded syntactic degree. In our result, we place no
restriction on the degree of the circuit.
Our algorithm is based on automata-theoretic ideas introduced in
[AMS08,AM08]. In those papers, the main idea was to construct deterministic
finite automata that isolate a single monomial from the set of nonzero
monomials of a polynomial in . In the present paper, since we need to deal with exponential degree
monomials, we carry out a different kind of monomial isolation using
nondeterministic automata.Comment: As the number of monomials in a noncommutative polynomial which has
anarithmetic circuit of size can actually be doubly exponential in ,
our result does not imply a randomized polynomial-time identity test for all
size s noncommutative circuits. The algorithm works only for noncommutative
size s circuits which computes a polynomial with exp(s) many monomial
Noncommutative Valiant's Classes: Structure and Complete Problems
In this paper we explore the noncommutative analogues, and
, of Valiant's algebraic complexity classes and show some
striking connections to classical formal language theory. Our main results are
the following: (1) We show that Dyck polynomials (defined from the Dyck
languages of formal language theory) are complete for the class
under reductions. Likewise, it turns out that
(Palindrome polynomials defined from palindromes) are complete
for the class (defined by polynomial-size skew circuits)
under reductions. The proof of these results is by suitably
adapting the classical Chomsky-Sch\"{u}tzenberger theorem showing that Dyck
languages are the hardest CFLs. (2) Next, we consider the class
. It is known~\cite{HWY10a} that, assuming the
sum-of-squares conjecture, the noncommutative polynomial
requires exponential size circuits. We
unconditionally show that is not
-complete under the projection reducibility. As a
consequence, assuming the sum-of-squares conjecture, we exhibit a strictly
infinite hierarchy of p-families under projections inside
(analogous to Ladner's theorem~\cite{Ladner75}). In the final section we
discuss some new -complete problems under
-reductions. (3) Inside too we show there is a
strict hierarchy of p-families (based on the nesting depth of Dyck polynomials)
under the reducibility
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