27,679 research outputs found
Succinct Representations for Abstract Interpretation
Abstract interpretation techniques can be made more precise by distinguishing
paths inside loops, at the expense of possibly exponential complexity.
SMT-solving techniques and sparse representations of paths and sets of paths
avoid this pitfall. We improve previously proposed techniques for guided static
analysis and the generation of disjunctive invariants by combining them with
techniques for succinct representations of paths and symbolic representations
for transitions based on static single assignment. Because of the
non-monotonicity of the results of abstract interpretation with widening
operators, it is difficult to conclude that some abstraction is more precise
than another based on theoretical local precision results. We thus conducted
extensive comparisons between our new techniques and previous ones, on a
variety of open-source packages.Comment: Static analysis symposium (SAS), Deauville : France (2012
Representing a P-complete problem by small trellis automata
A restricted case of the Circuit Value Problem known as the Sequential NOR
Circuit Value Problem was recently used to obtain very succinct examples of
conjunctive grammars, Boolean grammars and language equations representing
P-complete languages (Okhotin, http://dx.doi.org/10.1007/978-3-540-74593-8_23
"A simple P-complete problem and its representations by language equations",
MCU 2007). In this paper, a new encoding of the same problem is proposed, and a
trellis automaton (one-way real-time cellular automaton) with 11 states solving
this problem is constructed
Simple and Efficient Fully-Functional Succinct Trees
The fully-functional succinct tree representation of Navarro and Sadakane
(ACM Transactions on Algorithms, 2014) supports a large number of operations in
constant time using bits. However, the full idea is hard to
implement. Only a simplified version with operation time has been
implemented and shown to be practical and competitive. We describe a new
variant of the original idea that is much simpler to implement and has
worst-case time for the operations. An implementation based on
this version is experimentally shown to be superior to existing
implementations
Factorised Representations of Query Results
Query tractability has been traditionally defined as a function of input
database and query sizes, or of both input and output sizes, where the query
result is represented as a bag of tuples. In this report, we introduce a
framework that allows to investigate tractability beyond this setting. The key
insight is that, although the cardinality of a query result can be exponential,
its structure can be very regular and thus factorisable into a nested
representation whose size is only polynomial in the size of both the input
database and query.
For a given query result, there may be several equivalent representations,
and we quantify the regularity of the result by its readability, which is the
minimum over all its representations of the maximum number of occurrences of
any tuple in that representation. We give a characterisation of
select-project-join queries based on the bounds on readability of their results
for any input database. We complement it with an algorithm that can find
asymptotically optimal upper bounds and corresponding factorised
representations.Comment: 44 pages, 13 figure
Prospects and limitations of full-text index structures in genome analysis
The combination of incessant advances in sequencing technology producing large amounts of data and innovative bioinformatics approaches, designed to cope with this data flood, has led to new interesting results in the life sciences. Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems. These solutions include fast heuristic algorithms and advanced data structures, generally referred to as index structures. Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood. Moreover, the last decade has seen a boom in the number of variant index structures featuring complex and diverse memory-time trade-offs. This article brings a comprehensive state-of-the-art overview of the most popular index structures and their recently developed variants. Their features, interrelationships, the trade-offs they impose, but also their practical limitations, are explained and compared
Boundaries, defects and Frobenius algebras
The interpretation of D-branes in terms of open strings has lead to much
interest in boundary conditions of two-dimensional conformal field theories
(CFTs). These studies have deepened our understanding of CFT and allowed us to
develop new computational tools. The construction of CFT correlators based on
combining tools from topological field theory and non-commutative algebra in
tensor categories, which we summarize in this contribution, allows e.g. to
discuss, apart from boundary conditions, also defect lines and disorder fields.Comment: 7 pages. Contribution to the 35th International Symposium Ahrenshoop
on the Theory of Elementary Particles (Berlin, August 2002) and to the
International Conference on Theoretical Physics (UNESCO, Paris, July 2002).
For related proceedings contributions see
http://tpe.physik.rwth-aachen.de/schweigert/proceedings.htm
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