647 research outputs found
On Generalizing Decidable Standard Prefix Classes of First-Order Logic
Recently, the separated fragment (SF) of first-order logic has been
introduced. Its defining principle is that universally and existentially
quantified variables may not occur together in atoms. SF properly generalizes
both the Bernays-Sch\"onfinkel-Ramsey (BSR) fragment and the relational monadic
fragment. In this paper the restrictions on variable occurrences in SF
sentences are relaxed such that universally and existentially quantified
variables may occur together in the same atom under certain conditions. Still,
satisfiability can be decided. This result is established in two ways: firstly,
by an effective equivalence-preserving translation into the BSR fragment, and,
secondly, by a model-theoretic argument.
Slight modifications to the described concepts facilitate the definition of
other decidable classes of first-order sentences. The paper presents a second
fragment which is novel, has a decidable satisfiability problem, and properly
contains the Ackermann fragment and---once more---the relational monadic
fragment. The definition is again characterized by restrictions on the
occurrences of variables in atoms. More precisely, after certain
transformations, Skolemization yields only unary functions and constants, and
every atom contains at most one universally quantified variable. An effective
satisfiability-preserving translation into the monadic fragment is devised and
employed to prove decidability of the associated satisfiability problem.Comment: 34 page
A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment
Recently, the separated fragment (SF) has been introduced and proved to be
decidable. Its defining principle is that universally and existentially
quantified variables may not occur together in atoms. The known upper bound on
the time required to decide SF's satisfiability problem is formulated in terms
of quantifier alternations: Given an SF sentence
in which is quantifier free, satisfiability can be decided in
nondeterministic -fold exponential time. In the present paper, we conduct a
more fine-grained analysis of the complexity of SF-satisfiability. We derive an
upper and a lower bound in terms of the degree of interaction of existential
variables (short: degree)}---a novel measure of how many separate existential
quantifier blocks in a sentence are connected via joint occurrences of
variables in atoms. Our main result is the -NEXPTIME-completeness of the
satisfiability problem for the set of all SF sentences that have
degree or smaller. Consequently, we show that SF-satisfiability is
non-elementary in general, since SF is defined without restrictions on the
degree. Beyond trivial lower bounds, nothing has been known about the hardness
of SF-satisfiability so far.Comment: Full version of the LICS 2017 extended abstract having the same
title, 38 page
Deciding First-Order Satisfiability when Universal and Existential Variables are Separated
We introduce a new decidable fragment of first-order logic with equality,
which strictly generalizes two already well-known ones -- the
Bernays-Sch\"onfinkel-Ramsey (BSR) Fragment and the Monadic Fragment. The
defining principle is the syntactic separation of universally quantified
variables from existentially quantified ones at the level of atoms. Thus, our
classification neither rests on restrictions on quantifier prefixes (as in the
BSR case) nor on restrictions on the arity of predicate symbols (as in the
monadic case). We demonstrate that the new fragment exhibits the finite model
property and derive a non-elementary upper bound on the computing time required
for deciding satisfiability in the new fragment. For the subfragment of prenex
sentences with the quantifier prefix the
satisfiability problem is shown to be complete for NEXPTIME. Finally, we
discuss how automated reasoning procedures can take advantage of our results.Comment: Extended version of our LICS 2016 conference paper, 23 page
Closing the gap between atomic-scale lattice deformations and continuum elasticity
Crystal lattice deformations can be described microscopically by explicitly
accounting for the position of atoms or macroscopically by continuum
elasticity. In this work, we report on the description of continuous elastic
fields derived from an atomistic representation of crystalline structures that
also include features typical of the microscopic scale. Analytic expressions
for strain components are obtained from the complex amplitudes of the Fourier
modes representing periodic lattice positions, which can be generally provided
by atomistic modeling or experiments. The magnitude and phase of these
amplitudes, together with the continuous description of strains, are able to
characterize crystal rotations, lattice deformations, and dislocations.
Moreover, combined with the so-called amplitude expansion of the phase-field
crystal model, they provide a suitable tool for bridging microscopic to
macroscopic scales. This study enables the in-depth analysis of elasticity
effects for macro- and mesoscale systems taking microscopic details into
account.Comment: 9 pages, 7 figures, Supporting Information availabl
JAG: Reliable and Predictable Wireless Agreement under External Radio Interference
Wireless low-power transceivers used in sensor networks typically operate in unlicensed frequency bands that are subject to external radio interference caused by devices transmitting at much higher power.communication protocols should therefore be designed to be robust against such interference. A critical building block of many protocols at all layers is agreement on a piece of information among a set of nodes. At the MAC layer, nodes may need to agree on a new time slot or frequency channel, at the application layer nodes may need to agree on handing over a leader role from one node to another. Message loss caused by interference may break agreement in two different ways: none of the nodes uses the new information (time slot, channel, leader) and sticks with the previous assignment, or-even worse-some nodes use the new information and some do not. This may lead to reduced performance or failures. In this paper, we investigate the problem of agreement under external radio interference and point out the limitations of traditional message-based approaches. We propose JAG, a novel protocol that uses jamming instead of message transmissions to make sure that two neighbouring nodes agree, and show that it outperforms message-based approaches in terms of agreement probability, energy consumption, and time-to-completion. We further show that JAG can be used to obtain performance guarantees and meet the requirements of applications with real-time constraints.CONETReSens
Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model
One of the major difficulties in employing phase field crystal (PFC) modeling
and the associated amplitude (APFC) formulation is the ability to tune model
parameters to match experimental quantities. In this work we address the
problem of tuning the defect core and interface energies in the APFC
formulation. We show that the addition of a single term to the free energy
functional can be used to increase the solid-liquid interface and defect
energies in a well-controlled fashion, without any major change to other
features. The influence of the newly added term is explored in two-dimensional
triangular and honeycomb structures as well as bcc and fcc lattices in three
dimensions. In addition, a finite element method (FEM) is developed for the
model that incorporates a mesh refinement scheme. The combination of the FEM
and mesh refinement to simulate amplitude expansion with a new energy term
provides a method of controlling microscopic features such as defect and
interface energies while simultaneously delivering a coarse-grained examination
of the system.Comment: 14 pages, 9 figure
Drivers and Impacts in the Globalization of Corporate R&D: An Introduction Based on the European Experience
The globalization of R&D activities has continued its growth path as companies are increasingly trying to capture knowledge and market opportunities internationally. The rapid evolution of national economies and the ways to conduct knowledge-intensive businesses has led researchers and analysts to pursue a deeper understanding of the globalization of corporate R&D and the related driving factors and impacts. This introduction to the Special Section: "Globalization and Corporate R&D" forthcoming in Industrial and Corporate Change (vol. 20 (2), April 2011) provides an update of trends in the globalization of corporate R&D. It reviews the literature on the main drivers and impacts of the process under investigation, introduces the papers for this Special Section, and offers some concluding remarks.outsourcing, R&D, globalization, FDI
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