7,986 research outputs found
A General Framework for Sound and Complete Floyd-Hoare Logics
This paper presents an abstraction of Hoare logic to traced symmetric
monoidal categories, a very general framework for the theory of systems. Our
abstraction is based on a traced monoidal functor from an arbitrary traced
monoidal category into the category of pre-orders and monotone relations. We
give several examples of how our theory generalises usual Hoare logics (partial
correctness of while programs, partial correctness of pointer programs), and
provide some case studies on how it can be used to develop new Hoare logics
(run-time analysis of while programs and stream circuits).Comment: 27 page
Interest-based RDF Update Propagation
Many LOD datasets, such as DBpedia and LinkedGeoData, are voluminous and
process large amounts of requests from diverse applications. Many data products
and services rely on full or partial local LOD replications to ensure faster
querying and processing. While such replicas enhance the flexibility of
information sharing and integration infrastructures, they also introduce data
duplication with all the associated undesirable consequences. Given the
evolving nature of the original and authoritative datasets, to ensure
consistent and up-to-date replicas frequent replacements are required at a
great cost. In this paper, we introduce an approach for interest-based RDF
update propagation, which propagates only interesting parts of updates from the
source to the target dataset. Effectively, this enables remote applications to
`subscribe' to relevant datasets and consistently reflect the necessary changes
locally without the need to frequently replace the entire dataset (or a
relevant subset). Our approach is based on a formal definition for
graph-pattern-based interest expressions that is used to filter interesting
parts of updates from the source. We implement the approach in the iRap
framework and perform a comprehensive evaluation based on DBpedia Live updates,
to confirm the validity and value of our approach.Comment: 16 pages, Keywords: Change Propagation, Dataset Dynamics, Linked
Data, Replicatio
Resolving sets for Johnson and Kneser graphs
A set of vertices in a graph is a {\em resolving set} for if, for
any two vertices , there exists such that the distances . In this paper, we consider the Johnson graphs and Kneser
graphs , and obtain various constructions of resolving sets for these
graphs. As well as general constructions, we show that various interesting
combinatorial objects can be used to obtain resolving sets in these graphs,
including (for Johnson graphs) projective planes and symmetric designs, as well
as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems
and toroidal grids.Comment: 23 pages, 2 figures, 1 tabl
Locating regions in a sequence under density constraints
Several biological problems require the identification of regions in a
sequence where some feature occurs within a target density range: examples
including the location of GC-rich regions, identification of CpG islands, and
sequence matching. Mathematically, this corresponds to searching a string of 0s
and 1s for a substring whose relative proportion of 1s lies between given lower
and upper bounds. We consider the algorithmic problem of locating the longest
such substring, as well as other related problems (such as finding the shortest
substring or a maximal set of disjoint substrings). For locating the longest
such substring, we develop an algorithm that runs in O(n) time, improving upon
the previous best-known O(n log n) result. For the related problems we develop
O(n log log n) algorithms, again improving upon the best-known O(n log n)
results. Practical testing verifies that our new algorithms enjoy significantly
smaller time and memory footprints, and can process sequences that are orders
of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to
appear in SIAM Journal on Computin
Strong forms of linearization for Hopf monoids in species
A vector species is a functor from the category of finite sets with
bijections to vector spaces; informally, one can view this as a sequence of
-modules. A Hopf monoid (in the category of vector species) consists of a
vector species with unit, counit, product, and coproduct morphisms satisfying
several compatibility conditions, analogous to a graded Hopf algebra. We say
that a Hopf monoid is strongly linearized if it has a "basis" preserved by its
product and coproduct in a certain sense. We prove several equivalent
characterizations of this property, and show that any strongly linearized Hopf
monoid which is commutative and cocommutative possesses four bases which one
can view as analogues of the classical bases of the algebra of symmetric
functions. There are natural functors which turn Hopf monoids into graded Hopf
algebras, and applying these functors to strongly linearized Hopf monoids
produces several notable families of Hopf algebras. For example, in this way we
give a simple unified construction of the Hopf algebras of superclass functions
attached to the maximal unipotent subgroups of three families of classical
Chevalley groups.Comment: 35 pages; v2: corrected some typos, fixed attribution for Theorem
5.4.4; v3: some corrections, slight revisions, added references; v4: updated
references, numbering of results modified to conform with published version,
final versio
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