35 research outputs found
Cyclotomic Identity Testing and Applications
We consider the cyclotomic identity testing problem: given a polynomial
, decide whether is
zero, for a primitive complex -th root of unity and
integers . We assume that and are
represented in binary and consider several versions of the problem, according
to the representation of . For the case that is given by an algebraic
circuit we give a randomized polynomial-time algorithm with two-sided errors,
showing that the problem lies in BPP. In case is given by a circuit of
polynomially bounded syntactic degree, we give a randomized algorithm with
two-sided errors that runs in poly-logarithmic parallel time, showing that the
problem lies in BPNC. In case is given by a depth-2 circuit
(or, equivalently, as a list of monomials), we show that the cyclotomic
identity testing problem lies in NC. Under the generalised Riemann hypothesis,
we are able to extend this approach to obtain a polynomial-time algorithm also
for a very simple subclass of depth-3 circuits. We complement
this last result by showing that for a more general class of depth-3
circuits, a polynomial-time algorithm for the cyclotomic
identity testing problem would yield a sub-exponential-time algorithm for
polynomial identity testing. Finally, we use cyclotomic identity testing to
give a new proof that equality of compressed strings, i.e., strings presented
using context-free grammars, can be decided in coRNC: randomized NC with
one-sided errors
Compression by Contracting Straight-Line Programs
In grammar-based compression a string is represented by a context-free
grammar, also called a straight-line program (SLP), that generates only that
string. We refine a recent balancing result stating that one can transform an
SLP of size in linear time into an equivalent SLP of size so that
the height of the unique derivation tree is where is the length
of the represented string (FOCS 2019). We introduce a new class of balanced
SLPs, called contracting SLPs, where for every rule the string length of every variable on the right-hand side
is smaller by a constant factor than the string length of . In particular,
the derivation tree of a contracting SLP has the property that every subtree
has logarithmic height in its leaf size. We show that a given SLP of size
can be transformed in linear time into an equivalent contracting SLP of size
with rules of constant length.
We present an application to the navigation problem in compressed unranked
trees, represented by forest straight-line programs (FSLPs). We extend a linear
space data structure by Reh and Sieber (2020) by the operation of moving to the
-th child in time where is the degree of the current node.
Contracting SLPs are also applied to the finger search problem over
SLP-compressed strings where one wants to access positions near to a
pre-specified finger position, ideally in time where is the
distance between the accessed position and the finger. We give a linear space
solution where one can access symbols or move the finger in time for any constant where is the -fold
logarithm of . This improves a previous solution by Bille, Christiansen,
Cording, and G{\o}rtz (2018) with access/move time
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Faculty Publications and Creative Works 2005
Faculty Publications & Creative Works is an annual compendium of scholarly and creative activities of University of New Mexico faculty during the noted calendar year. Published by the Office of the Vice President for Research and Economic Development, it serves to illustrate the robust and active intellectual pursuits conducted by the faculty in support of teaching and research at UNM. In 2005, UNM faculty produced over 1,887 works, including 1,887 scholarly papers and articles, 57 books, 127 book chapters, 58 reviews, 68 creative works and 4 patented works. We are proud of the accomplishments of our faculty which are in part reflected in this book, which illustrates the diversity of intellectual pursuits in support of research and education at the University of New Mexico
Evolutionary Computation
This book presents several recent advances on Evolutionary Computation, specially evolution-based optimization methods and hybrid algorithms for several applications, from optimization and learning to pattern recognition and bioinformatics. This book also presents new algorithms based on several analogies and metafores, where one of them is based on philosophy, specifically on the philosophy of praxis and dialectics. In this book it is also presented interesting applications on bioinformatics, specially the use of particle swarms to discover gene expression patterns in DNA microarrays. Therefore, this book features representative work on the field of evolutionary computation and applied sciences. The intended audience is graduate, undergraduate, researchers, and anyone who wishes to become familiar with the latest research work on this field
Détection et analyse de motifs structuraux et fonctionnels dans les acides ribonucléiques
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal
Technology for large space systems: A bibliography with indexes (supplement 22)
This bibliography lists 1077 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System between July 1, 1989 and December 31, 1989. Its purpose is to provide helpful information to the researcher or manager engaged in the development of technologies related to large space systems. Subject areas include mission and program definition, design techniques, structural and thermal analysis, structural dynamics and control systems, electronics, advanced materials, assembly concepts, and propulsion
Space station systems: A bibliography with indexes (supplement 10)
This bibliography lists 1,422 reports, articles, and other documents introduced into the NASA scientific and technical information system between July 1, 1989 and December 31, 1989. Its purpose is to provide helpful information to researchers, designers and managers engaged in Space Station technology development and mission design. Coverage includes documents that define major systems and subsystems related to structures and dynamic control, electronics and power supplies, propulsion, and payload integration. In addition, orbital construction methods, servicing and support requirements, procedures and operations, and missions for the current and future Space Station are included