2,883 research outputs found
Interaction Testing, Fault Location, and Anonymous Attribute-Based Authorization
abstract: This dissertation studies three classes of combinatorial arrays with practical applications in testing, measurement, and security. Covering arrays are widely studied in software and hardware testing to indicate the presence of faulty interactions. Locating arrays extend covering arrays to achieve identification of the interactions causing a fault by requiring additional conditions on how interactions are covered in rows. This dissertation introduces a new class, the anonymizing arrays, to guarantee a degree of anonymity by bounding the probability a particular row is identified by the interaction presented. Similarities among these arrays lead to common algorithmic techniques for their construction which this dissertation explores. Differences arising from their application domains lead to the unique features of each class, requiring tailoring the techniques to the specifics of each problem.
One contribution of this work is a conditional expectation algorithm to build covering arrays via an intermediate combinatorial object. Conditional expectation efficiently finds intermediate-sized arrays that are particularly useful as ingredients for additional recursive algorithms. A cut-and-paste method creates large arrays from small ingredients. Performing transformations on the copies makes further improvements by reducing redundancy in the composed arrays and leads to fewer rows.
This work contains the first algorithm for constructing locating arrays for general values of and . A randomized computational search algorithmic framework verifies if a candidate array is -locating by partitioning the search space and performs random resampling if a candidate fails. Algorithmic parameters determine which columns to resample and when to add additional rows to the candidate array. Additionally, analysis is conducted on the performance of the algorithmic parameters to provide guidance on how to tune parameters to prioritize speed, accuracy, or a combination of both.
This work proposes anonymizing arrays as a class related to covering arrays with a higher coverage requirement and constraints. The algorithms for covering and locating arrays are tailored to anonymizing array construction. An additional property, homogeneity, is introduced to meet the needs of attribute-based authorization. Two metrics, local and global homogeneity, are designed to compare anonymizing arrays with the same parameters. Finally, a post-optimization approach reduces the homogeneity of an anonymizing array.Dissertation/ThesisDoctoral Dissertation Computer Science 201
Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
We introduce the notion of the stopping redundancy hierarchy of a linear
block code as a measure of the trade-off between performance and complexity of
iterative decoding for the binary erasure channel. We derive lower and upper
bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and
Bonferroni-type inequalities, and specialize them for codes with cyclic
parity-check matrices. Based on the observed properties of parity-check
matrices with good stopping redundancy characteristics, we develop a novel
decoding technique, termed automorphism group decoding, that combines iterative
message passing and permutation decoding. We also present bounds on the
smallest number of permutations of an automorphism group decoder needed to
correct any set of erasures up to a prescribed size. Simulation results
demonstrate that for a large number of algebraic codes, the performance of the
new decoding method is close to that of maximum likelihood decoding.Comment: 40 pages, 6 figures, 10 tables, submitted to IEEE Transactions on
Information Theor
Commutative association schemes
Association schemes were originally introduced by Bose and his co-workers in
the design of statistical experiments. Since that point of inception, the
concept has proved useful in the study of group actions, in algebraic graph
theory, in algebraic coding theory, and in areas as far afield as knot theory
and numerical integration. This branch of the theory, viewed in this collection
of surveys as the "commutative case," has seen significant activity in the last
few decades. The goal of the present survey is to discuss the most important
new developments in several directions, including Gelfand pairs, cometric
association schemes, Delsarte Theory, spin models and the semidefinite
programming technique. The narrative follows a thread through this list of
topics, this being the contrast between combinatorial symmetry and
group-theoretic symmetry, culminating in Schrijver's SDP bound for binary codes
(based on group actions) and its connection to the Terwilliger algebra (based
on combinatorial symmetry). We propose this new role of the Terwilliger algebra
in Delsarte Theory as a central topic for future work.Comment: 36 page
Construction of nested space-filling designs
New types of designs called nested space-filling designs have been proposed
for conducting multiple computer experiments with different levels of accuracy.
In this article, we develop several approaches to constructing such designs.
The development of these methods also leads to the introduction of several new
discrete mathematics concepts, including nested orthogonal arrays and nested
difference matrices.Comment: Published in at http://dx.doi.org/10.1214/09-AOS690 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A polynomial construction of perfect sequence covering arrays
A PSCA is a multiset of permutations of the -element
alphabet such that every sequence of distinct elements
of the alphabet appears in the specified order in exactly
permutations. For , let be the smallest positive integer
such that a PSCA exists. We present an explicit
construction that proves for fixed . The
method of construction involves taking a permutation representation of the
group of projectivities of a suitable projective space of dimension and
deleting all but a certain number of symbols from each permutation. In the case
that this space is a Desarguesian projective plane, we also show that there
exists a permutation representation of the group of projectivities of the plane
that covers the vast majority of 4-sequences of its points a fixed number of
times
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary one-error-correcting codes of
length 15 as well as their extensions of length 16 was recently carried out in
[P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary
one-error-correcting codes of length 15: Part I--Classification," IEEE Trans.
Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying
work, the classified codes are studied in great detail, and their main
properties are tabulated. The results include the fact that 33 of the 80
Steiner triple systems of order 15 occur in such codes. Further understanding
is gained on full-rank codes via switching, as it turns out that all but two
full-rank codes can be obtained through a series of such transformations from
the Hamming code. Other topics studied include (non)systematic codes, embedded
one-error-correcting codes, and defining sets of codes. A classification of
certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of
coordinates fixed by symmetries of codes), added and extended many other
result
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