156,500 research outputs found
Learning conversions in science: The case of vocational students in the UK
The paper describes two aspects of a research project that focused on vocational science students. The paper begins with a general description of vocational science in the UK, to put the work in context. It then outlines an analysis of the ways in which these students approach problems involving converting between units of measurement. Finally the development and evaluation of computer‐based activities designed to support students in learning about unit conversion are described
Canonized Rewriting and Ground AC Completion Modulo Shostak Theories : Design and Implementation
AC-completion efficiently handles equality modulo associative and commutative
function symbols. When the input is ground, the procedure terminates and
provides a decision algorithm for the word problem. In this paper, we present a
modular extension of ground AC-completion for deciding formulas in the
combination of the theory of equality with user-defined AC symbols,
uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. Our
algorithm, called AC(X), is obtained by augmenting in a modular way ground
AC-completion with the canonizer and solver present for the theory X. This
integration rests on canonized rewriting, a new relation reminiscent to
normalized rewriting, which integrates canonizers in rewriting steps. AC(X) is
proved sound, complete and terminating, and is implemented to extend the core
of the Alt-Ergo theorem prover.Comment: 30 pages, full version of the paper TACAS'11 paper "Canonized
Rewriting and Ground AC-Completion Modulo Shostak Theories" accepted for
publication by LMCS (Logical Methods in Computer Science
Embedded Cobordism Categories and Spaces of Manifolds
Galatius, Madsen, Tillmann and Weiss have identified the homotopy type of the
classifying space of the cobordism category with objects (d-1)-dimensional
manifolds embedded in R^\infty. In this paper we apply the techniques of spaces
of manifolds, as developed by the author and Galatius, to identify the homotopy
type of the cobordism category with objects (d-1)-dimensional submanifolds of a
fixed background manifold M.
There is a description in terms of a space of sections of a bundle over M
associated to its tangent bundle. This can be interpreted as a form of Poincare
duality, relating a space of submanifolds of M to a space of functions on M
String rewriting for Double Coset Systems
In this paper we show how string rewriting methods can be applied to give a
new method of computing double cosets. Previous methods for double cosets were
enumerative and thus restricted to finite examples. Our rewriting methods do
not suffer this restriction and we present some examples of infinite double
coset systems which can now easily be solved using our approach. Even when both
enumerative and rewriting techniques are present, our rewriting methods will be
competitive because they i) do not require the preliminary calculation of
cosets; and ii) as with single coset problems, there are many examples for
which rewriting is more effective than enumeration.
Automata provide the means for identifying expressions for normal forms in
infinite situations and we show how they may be constructed in this setting.
Further, related results on logged string rewriting for monoid presentations
are exploited to show how witnesses for the computations can be provided and
how information about the subgroups and the relations between them can be
extracted. Finally, we discuss how the double coset problem is a special case
of the problem of computing induced actions of categories which demonstrates
that our rewriting methods are applicable to a much wider class of problems
than just the double coset problem.Comment: accepted for publication by the Journal of Symbolic Computatio
Coherent presentations of Artin monoids
We compute coherent presentations of Artin monoids, that is presentations by
generators, relations, and relations between the relations. For that, we use
methods of higher-dimensional rewriting that extend Squier's and Knuth-Bendix's
completions into a homotopical completion-reduction, applied to Artin's and
Garside's presentations. The main result of the paper states that the so-called
Tits-Zamolodchikov 3-cells extend Artin's presentation into a coherent
presentation. As a byproduct, we give a new constructive proof of a theorem of
Deligne on the actions of an Artin monoid on a category
Gluing Localized Mirror Functors
We develop a method of gluing the local mirrors and functors constructed from
immersed Lagrangians in the same deformation class. As a result, we obtain a
global mirror geometry and a canonical mirror functor. We apply the method to
construct the mirrors of punctured Riemann surfaces and show that our functor
derives homological mirror symmetry.Comment: 69 pages, 39 figures, comments are welcom
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