1,414 research outputs found
Existentially restricted quantified constraint satisfaction
AbstractThe quantified constraint satisfaction problem (QCSP) is a framework for modelling PSPACE computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In this paper, we introduce and study a new model for investigating QCSP complexity in which the types of constraints given by the existentially quantified variables, is restricted. Our primary technical contribution is the development and application of a general technology for proving positive results on parameterizations of the model, of inclusion in the complexity class coNP
On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type
We provide a comprehensive analysis of sharp bilinear estimates of
Ozawa-Tsutsumi type for solutions u of the free Schr\"odinger equation, which
give sharp control on in classical Sobolev spaces. In particular, we
provide a generalization of their estimates in such a way that provides a
unification with some sharp bilinear estimates proved by Carneiro and
Planchon-Vega, via entirely different methods, by seeing them all as special
cases of a one parameter family of sharp estimates. We show that the extremal
functions are solutions of the Maxwell-Boltzmann functional equation and
provide a new proof that this equation admits only Gaussian solutions. We also
make a connection to certain sharp estimates on involving certain
dispersive Sobolev norms.Comment: 17 pages, references update
Recommended from our members
Signposting to excellence: Treating patients with Dementia
In order to help dental clinicians working with patients showing signs of dementia the Faculty of General Dental Practice (FGDP) has a new publication; ‘Dementia Friendly Dentistry. Good Practice Guidelines’, edited by Paul Batchelor (2017). This small ring bound book has been developed with input from dementia support organisations, including the Alzheimer’s Society, Healthwatch England, and the London Dementia Clinical Network. This type of collaboration with those outside of dentistry has led to the production of a comprehensive guide that looks at this life limiting illness from a broad perspective that can sometime be missed in dental only publications. As such, this set of guidelines will be useful to new and experienced dental professionals alike and joins the other four similar publications from the FGDP
Algebraic Properties of Valued Constraint Satisfaction Problem
The paper presents an algebraic framework for optimization problems
expressible as Valued Constraint Satisfaction Problems. Our results generalize
the algebraic framework for the decision version (CSPs) provided by Bulatov et
al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties
and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP
languages to weighted algebras. We show that the difficulty of VCSP depends
only on the weighted variety generated by the associated weighted algebra.
Paralleling the results for CSPs we exhibit a reduction to cores and rigid
cores which allows us to focus on idempotent weighted varieties. Further, we
propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the
hardness direction and verify that it agrees with known results for VCSPs on
two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny
2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author
- …