47,155 research outputs found
Interpretations of Presburger Arithmetic in Itself
Presburger arithmetic PrA is the true theory of natural numbers with
addition. We study interpretations of PrA in itself. We prove that all
one-dimensional self-interpretations are definably isomorphic to the identity
self-interpretation. In order to prove the results we show that all linear
orders that are interpretable in (N,+) are scattered orders with the finite
Hausdorff rank and that the ranks are bounded in terms of the dimension of the
respective interpretations. From our result about self-interpretations of PrA
it follows that PrA isn't one-dimensionally interpretable in any of its finite
subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201
The strength of countable saturation
We determine the proof-theoretic strength of the principle of countable
saturation in the context of the systems for nonstandard arithmetic introduced
in our earlier work.Comment: Corrected typos in Lemma 3.4 and the final paragraph of the
conclusio
Arithmetic lattices and weak spectral geometry
This note is an expansion of three lectures given at the workshop "Topology,
Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University
in December of 2006 and will appear in the proceedings for this workshop.Comment: To appear in workshop proceedings for "Topology, Complex Analysis and
Arithmetic of Hyperbolic Spaces". Comments welcom
Conjectures on the logarithmic derivatives of Artin L-functions II
We formulate a general conjecture relating Chern classes of subbundles of
Gauss-Manin bundles in Arakelov geometry to logarithmic derivatives of Artin
L-functions of number fields. This conjecture may be viewed as a far-reaching
generalisation of the (Lerch-)Chowla-Selberg formula computing logarithms of
periods of elliptic curves in terms of special values of the -function.
We prove several special cases of this conjecture in the situation where the
involved Artin characters are Dirichlet characters. This article contains the
computations promised in the article {\it Conjectures sur les d\'eriv\'ees
logarithmiques des fonctions L d'Artin aux entiers n\'egatifs}, where our
conjecture was announced. We also give a quick introduction to the
Grothendieck-Riemann-Roch theorem and to the geometric fixed point formula,
which form the geometric backbone of our conjecture.Comment: 54 page
Hurwitz ball quotients
We consider the analogue of Hurwitz curves, smooth projective curves of
genus that realize equality in the Hurwitz bound , to smooth compact quotients of the unit ball in
. When is arithmetic, we show that , where is the (topological) Euler characteristic, and in the case
of equality show that is a regular cover of a particular Deligne--Mostow
orbifold. We conjecture that this inequality holds independent of
arithmeticity, and note that work of Xiao makes progress on this conjecture and
implies the best-known lower bound for the volume of a complex hyperbolic
-orbifold.Comment: Several improvements incorporating referee's comments. To appear in
Math.
Verification of Hierarchical Artifact Systems
Data-driven workflows, of which IBM's Business Artifacts are a prime
exponent, have been successfully deployed in practice, adopted in industrial
standards, and have spawned a rich body of research in academia, focused
primarily on static analysis. The present work represents a significant advance
on the problem of artifact verification, by considering a much richer and more
realistic model than in previous work, incorporating core elements of IBM's
successful Guard-Stage-Milestone model. In particular, the model features task
hierarchy, concurrency, and richer artifact data. It also allows database key
and foreign key dependencies, as well as arithmetic constraints. The results
show decidability of verification and establish its complexity, making use of
novel techniques including a hierarchy of Vector Addition Systems and a variant
of quantifier elimination tailored to our context.Comment: Full version of the accepted PODS pape
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