859 research outputs found
Loop-fusion cohomology and transgression
`Loop-fusion cohomology' is defined on the continuous loop space of a
manifold in terms of \vCech cochains satisfying two multiplicative conditions
with respect to the fusion and figure-of-eight products on loops. The main
result is that these cohomology groups, with coefficients in an abelian group,
are isomorphic to those of the manifold and the transgression homomorphism
factors through the isomorphism.Comment: 10 pages. v2 contains minor correction
Node Labels in Local Decision
The role of unique node identifiers in network computing is well understood
as far as symmetry breaking is concerned. However, the unique identifiers also
leak information about the computing environment - in particular, they provide
some nodes with information related to the size of the network. It was recently
proved that in the context of local decision, there are some decision problems
such that (1) they cannot be solved without unique identifiers, and (2) unique
node identifiers leak a sufficient amount of information such that the problem
becomes solvable (PODC 2013).
In this work we give study what is the minimal amount of information that we
need to leak from the environment to the nodes in order to solve local decision
problems. Our key results are related to scalar oracles that, for any given
, provide a multiset of labels; then the adversary assigns the
labels to the nodes in the network. This is a direct generalisation of the
usual assumption of unique node identifiers. We give a complete
characterisation of the weakest oracle that leaks at least as much information
as the unique identifiers.
Our main result is the following dichotomy: we classify scalar oracles as
large and small, depending on their asymptotic behaviour, and show that (1) any
large oracle is at least as powerful as the unique identifiers in the context
of local decision problems, while (2) for any small oracle there are local
decision problems that still benefit from unique identifiers.Comment: Conference version to appear in the proceedings of SIROCCO 201
Classes of Terminating Logic Programs
Termination of logic programs depends critically on the selection rule, i.e.
the rule that determines which atom is selected in each resolution step. In
this article, we classify programs (and queries) according to the selection
rules for which they terminate. This is a survey and unified view on different
approaches in the literature. For each class, we present a sufficient, for most
classes even necessary, criterion for determining that a program is in that
class. We study six classes: a program strongly terminates if it terminates for
all selection rules; a program input terminates if it terminates for selection
rules which only select atoms that are sufficiently instantiated in their input
positions, so that these arguments do not get instantiated any further by the
unification; a program local delay terminates if it terminates for local
selection rules which only select atoms that are bounded w.r.t. an appropriate
level mapping; a program left-terminates if it terminates for the usual
left-to-right selection rule; a program exists-terminates if there exists a
selection rule for which it terminates; finally, a program has bounded
nondeterminism if it only has finitely many refutations. We propose a
semantics-preserving transformation from programs with bounded nondeterminism
into strongly terminating programs. Moreover, by unifying different formalisms
and making appropriate assumptions, we are able to establish a formal hierarchy
between the different classes.Comment: 50 pages. The following mistake was corrected: In figure 5, the first
clause for insert was insert([],X,[X]
Geoarchaeological Approaches to Pictish Settlement Sites: Assessing Heritage at Risk
Due to the poor preservation of Pictish period buildings and the occupation deposits within them, very little is known of daily life in early medieval Scotland. In lowland and coastal areas, Pictish buildings are generally truncated by deep ploughing, coastal erosion, or urban development, while those uncovered in upland areas seem to have no preserved floor deposits for reasons that remain poorly understood. Geoarchaeological techniques are particularly effective in clarifying site formation processes and understanding post-depositional transformations. They are also a powerful research tool for identifying floor deposits, distinguishing their composition, and linking this to daily activities. However, archaeologists are often reluctant to apply geoarchaeological methods if they suspect preservation is poor or stratigraphy is not visible in the field.
This study therefore employs an innovative suite of geoarchaeological techniques to evaluate the preservation of Pictish period buildings and the potential that fragmentary buildings have to reconstruct daily life in early medieval Scotland. Alongside literature analysis and a desk-based comparison with national soil datasets, over 400 sediment samples from three key settlement sites were subjected to integrated soil micromorphology, x-ray fluorescence, magnetic susceptibility, loss-on-ignition, pH, electrical conductivity and microrefuse analysis. The combined data were successful in generating new information about the depositional and post-depositional history of the sites, preservation conditions of the occupation deposits, and activity areas within domestic dwellings. Most significantly, the integrated approach demonstrated that ephemeral and fragmented occupation surfaces retain surviving characteristics of the use of space, even if floors are not preserved well enough to be clearly defined in the field or in thin-section. A partnership with Historic Environment Scotland has channelled this work into research-led guidelines aimed at communicating geoarchaeological methods and principles to a wider audience
On the Complexity of Computing Minimal Unsatisfiable LTL formulas
We show that (1) the Minimal False QCNF search-problem (MF-search) and the
Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE
complete because of the very expressive power of QBF/LTL, (2) we extend the
PSPACE-hardness of the MF decision problem to the MU decision problem. As a
consequence, we deduce a positive answer to the open question of PSPACE
hardness of the inherent Vacuity Checking problem. We even show that the
Inherent Non Vacuous formula search problem is also FPSPACE-complete.Comment: Minimal unsatisfiable cores For LTL causes inherent vacuity checking
redundancy coverag
AC-KBO Revisited
Equational theories that contain axioms expressing associativity and
commutativity (AC) of certain operators are ubiquitous. Theorem proving methods
in such theories rely on well-founded orders that are compatible with the AC
axioms. In this paper we consider various definitions of AC-compatible
Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are
revisited. The former is enhanced to a more powerful version, and we modify the
latter to amend its lack of monotonicity on non-ground terms. We further
present new complexity results. An extension reflecting the recent proposal of
subterm coefficients in standard Knuth-Bendix orders is also given. The various
orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming
(TPLP) special issue for the 12th International Symposium on Functional and
Logic Programming (FLOPS 2014
Description logics of context
We introduce Description Logics of Context (DLCs)—an extension of Description Logics (DLs) for context-based reasoning. Our approach descends from J. McCarthy's tradition of treating contexts as formal objects over which one can quantify and express first-order properties. DLCs are founded in two-dimensional possible world semantics, where one dimension represents a usual object domain and the other a domain of contexts, and accommodate two interacting DL languages—the object and the context language—interpreted over their respective domains. Effectively, DLCs comprise a family of two-sorted , two-dimensional combinations of pairs of DLs. We argue that this setup ensures a well-grounded, generic framework for capturing and studying mechanisms of contextualization in the DL paradigm. As the main technical contribution, we prove 2ExpTime-completeness of the satisfiability problem in the maximally expressive DLC, based on the DL forumla . As an interesting corollary, we show that under certain conditions this result holds also for a range of two-dimensional DLs, including the prominent forumla
Architectural Refinement in HETS
The main objective of this work is to bring a number of improvements to the Heterogeneous Tool Set HETS, both from a theoretical and an implementation point of view. In the first part of the thesis we present a number of recent extensions of the tool, among which declarative specifications of logics, generalized theoroidal comorphisms, heterogeneous colimits and integration of the logic of the term rewriting system Maude. In the second part we concentrate on the CASL architectural refinement language, that we equip with a notion of refinement tree and with calculi for checking correctness and consistency of refinements. Soundness and completeness of these calculi is also investigated. Finally, we present the integration of the VSE refinement method in HETS as an institution comorphism. Thus, the proof manangement component of HETS remains unmodified
On the equivalence between Lurie's model and the dendroidal model for infinity-operads
© 2016 Elsevier Inc.We compare two approaches to the homotopy theory of ∞-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets and ∞-categories which replaces simplices by trees. The other is based on a certain homotopy theory of marked simplicial sets over the nerve of Segal's category Γ. In this paper we prove that for operads without constants these two theories are equivalent, in the precise sense of the existence of a zig-zag of Quillen equivalences between the respective model categories
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