372 research outputs found
The category of MSO transductions
MSO transductions are binary relations between structures which are defined
using monadic second-order logic. MSO transductions form a category, since they
are closed under composition. We show that many notions from language theory,
such as recognizability or tree decompositions, can be defined in an abstract
way that only refers to MSO transductions and their compositions
An approach to categorification of some small quantum groups II
We categorify an idempotented form of quantum sl2 and some of its simple
representations at a prime root of unity.Comment: 59 pages, many PSTricks figures, v2 contains minor corrections and
updated reference
Monadic second-order model-checking on decomposable matroids
A notion of branch-width, which generalizes the one known for graphs, can be
defined for matroids. We first give a proof of the polynomial time
model-checking of monadic second-order formulas on representable matroids of
bounded branch-width, by reduction to monadic second-order formulas on trees.
This proof is much simpler than the one previously known. We also provide a
link between our logical approach and a grammar that allows to build matroids
of bounded branch-width. Finally, we introduce a new class of non-necessarily
representable matroids, described by a grammar and on which monadic
second-order formulas can be checked in linear time.Comment: 32 pages, journal paper. Revision: the last part has been removed and
the writing improve
Lagrangian Reachabililty
We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that
conservatively approximates the set of reachable states of a nonlinear
dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF),
which is derived from an over-approximation of the gradient of the solution
flows. The SF measures the discrepancy between two states propagated by the
system solution from two initial states lying in a well-defined region, thereby
allowing LRT to compute a reachtube with a ball-overestimate in a metric where
the computed enclosure is as tight as possible. To evaluate its performance, we
implemented a prototype of LRT in C++/Matlab, and ran it on a set of
well-established benchmarks. Our results show that LRT compares very favorably
with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201
Equivariant dendroidal sets and simplicial operads
We establish a Quillen equivalence between the homotopy theories of
equivariant Segal operads and equivariant simplicial operads with norm maps.
Together with previous work, we further conclude that the homotopy coherent
nerve is a right-Quillen equivalence from the model category of equivariant
simplicial operads with norm maps to the model category structure for
equivariant--operads in equivariant dendroidal sets.Comment: v3: Improvements to exposition and minor edits, in response to
referee suggestion
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