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Nested interpolants

Matthias Heizmann, Jochen Hoenicke, Andreas Podelski
2010 SIGPLAN notices  
The method avoids the costly construction of the abstract transformer by constructing a nested word automaton from an inductive sequence of 'nested interpolants' (i.e., interpolants for a nested word which  ...  Our technical contribution is an interpolant-based software model checking method for recursive programs.  ...  Canonical Interpolant Automaton We use an inductive sequence of nested interpolants for a nested error trace π to construct a nested interpolant automaton.  ... 
doi:10.1145/1707801.1706353 fatcat:zsxqnmbb5nd5pfw6ewoo3we2xu

Interpolation in nest algebra modules

Xiaoxia Zhang
2001 Proceedings of the American Mathematical Society  
Let A be a nest algebra and LatA its invariant projection (or subspace) lattice.  ...  In this paper, we consider the operator interpolation problem in the case of a nest algebra module.  ...  In [5] the authors solved this problem in nest algebra and gave a sufficient and necessary condition. We call this case operator interpolation.  ... 
doi:10.1090/s0002-9939-01-06074-9 fatcat:ciiuhkwu75hetpceoanljn2bqa

Interpolating Operators in Nest Algebras

M. Anoussis
1992 Proceedings of the American Mathematical Society  
Given two families {xa}, {ya} of vectors and a nest Jf in a Hubert space H, we provide a necessary and sufficient condition for the existence of an operator T in the nest algebra satisfying Txa = ya for  ...  Other questions about interpolating operators are investigated in [1, 4] .  ...  Given two families of vectors {xQ}, {ya} in a Hubert space, an interpolating operator is a bounded operator T such that Txa = ya for every a.  ... 
doi:10.2307/2159393 fatcat:g7wong4wnrhyjm65o4e3zwodyy

Modal interpolation via nested sequents

Melvin Fitting, Roman Kuznets
2015 Annals of Pure and Applied Logic  
by enumerating all theorems until an interpolant is found.  ...  The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems.  ...  Theory, Applications and Tools" at the Vienna Summer of Logic 2014, who witnessed the various stages of the development of this paper, from the earliest versions that used prefixed tableaux rather than nested  ... 
doi:10.1016/j.apal.2014.11.002 fatcat:raymvqfoh5gctnbxz2uoi27zgq

Interpolation problems in nest algebras

William Arveson
1975 Journal of Functional Analysis  
THE INTERPOLATION THEOREM In this paper, however, we are concerned with nest algebras, which are neither self-adjoint nor commutative.  ...  As in [6] , this type of result will be called an interpolation theorem, by virtue of the analogy with certain interpolation problems in algebras of bounded analytic functions.  ... 
doi:10.1016/0022-1236(75)90041-5 fatcat:getl2hrtarayffaehzaagyofai

Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis

Steffen Börm, Jens M. Melenk
2017 Numerische Mathematik  
The scheme is based on polynomial interpolation combined with suitable pre- and postmultiplication by plane waves.  ...  Numerical experiments In order to investigate how accurately our theoretical results predict the convergence of an actual implementation of our nested interpolation scheme, we have implemented a Table  ...  In order to obtain the polylogarithmic-linear complexity, we require an approximation that uses nested expansion systems.  ... 
doi:10.1007/s00211-017-0873-y fatcat:5qu7xtwhojh2djdl3p26xdnmdm

Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents [article]

Tim Lyon, Alwen Tiu, Rajeev Goré, Ranald Clouston
2019 arXiv   pre-print
These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi.  ...  A novel feature of our proof includes an orthogonality condition for defining duality between interpolants.  ...  One solution to this problem is to generalise the interpolation statement to consider a nested sequent as an interpolant: If a nested sequent ⊢ Γ is provable, then for every 'partitioning' of ⊢ Γ into  ... 
arXiv:1910.05215v2 fatcat:f5yrncqo4vhrhclzjr6d6mzqli

Ranking spatial interpolation techniques using a GIS-based DSS

2013 Global NEST Journal  
A GIS-based Decision Support System (DSS) was developed to select the appropriate interpolation technique used in studying rainfall spatial variability.  ...  Vol 6, No 1, pp 1-20, 2004 Copyright© 2004 GLOBAL NEST Printed in Greece. All rights reserved RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED DSS hydrologic and management models.  ...  over an area (e.g. a catchment) based on the results of meteorological observations, motivated the development of gridded estimates of precipitation to provide inputs to spatially distributed Global Nest  ... 
doi:10.30955/gnj.000224 fatcat:vwbwuyxgdfbchloblzcj7exym4

Interpolation for Intermediate Logics via Hyper- and Linear Nested Sequents

Roman Kuznets, Björn Lellmann
2018 Advances in Modal Logic  
To tackle the latter, we switch to linear nested sequents, demonstrate syntactic cut elimination for them, and use it to prove interpolation for Gödel logic.  ...  The goal of this paper is extending to intermediate logics the constructive prooftheoretic method of proving Craig and Lyndon interpolation via hypersequents and nested sequents developed earlier for classical  ...  In particular, a linear nested calculus would not help prove interpolation in the modal case. The exact source of this disparity deserves further investigation.  ... 
dblp:conf/aiml/KuznetsL18 fatcat:e6peqamkvvae5gx5hahuyv2l3i

On a conjecture of Tomas Sauer regarding nested ideal interpolation

Boris Shekhtman
2008 Proceedings of the American Mathematical Society  
It follows that there does not exist a "continuous" Newton form for multivariate interpolation, hence a "continuous" notion of multivariate divided differences.  ...  Discussion In this section we wish to discuss some implications that the above example has in the theory of ideal interpolation and the Newton form for multivariate ideal projectors.  ... 
doi:10.1090/s0002-9939-08-09816-x fatcat:fk5wj6zk6nd2nlroirfphgav7i

Intercomparison of Spatial Interpolation Schemes for Use in Nested Grid Models

Kiran Alapaty, Rohit Mathur, Talat Odman
1998 Monthly Weather Review  
Two geometrical and two advection-equivalent spatial interpolation schemes were tested in providing lateral boundary conditions to a nested grid domain.  ...  Geometric interpolation schemes used in this study are a zerothorder and a quadratic scheme, while the two advection-equivalent interpolation schemes were based on upwind and Bott's advection schemes.  ...  Quadratic interpolation scheme The quadratic interpolation scheme is based on the conservation formula for nested grids suggested by Kurihara et al. (1979) and Clark and Farley (1984) .  ... 
doi:10.1175/1520-0493(1998)126<0243:iosisf>2.0.co;2 fatcat:z2brw7ikfnhchmmpcpl5i4oibu

Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents

Tim Lyon, Alwen Tiu, Rajeev Goré, Ranald Clouston, Michael Wagner
2020 Annual Conference for Computer Science Logic  
These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi.  ...  A novel feature of our proof includes an orthogonality condition for defining duality between interpolants.  ...  We have presented a novel approach to proving the interpolation theorem for a range of logics possessing a nested sequent calculus.  ... 
doi:10.4230/lipics.csl.2020.28 dblp:conf/csl/LyonTGC20 fatcat:iiufl64qlngjri3oayorwa4wpu

A Two-Way Nesting Unstructured Quadrilateral Grid, Finite-Differencing, Estuarine and Coastal Ocean Model with High-Order Interpolation Schemes

Zhangliang Ding, Jianrong Zhu, Bingrui Chen, Daoyang Bao
2021 Journal of Marine Science and Engineering  
The model is novel for two interpolation schemes: the high-order spatial interpolation at the middle temporal level (HSIMT) parabolic interpolation scheme and HSIMT advection-equivalent interpolation scheme  ...  , which are interpolated or updated from actual grid variables.  ...  Interpolation Schemes In contrast to update schemes, plenty of interpolation schemes have been used in nested grid models [33] .  ... 
doi:10.3390/jmse9030335 fatcat:5wi2bq2hkjeqtkhcoqqm2fk5hi

Interpolating Population Distributions using Public-use Data: An Application to Income Segregation using American Community Survey Data [article]

Matthew Simpson, Scott H. Holan, Christopher K. Wikle, Jonathan R. Bradley
2021 arXiv   pre-print
We propose a model-based method to interpolate estimates of features of the income distribution that accounts for this error.  ...  Each PUMA is designed to contain around 100, 000 people, and census tracts are nested within PUMAs.  ...  Estimation and interpolation To construct estimates of any feature of the distribution of interest, including interpolating between the end points of the bins, we will use the Bayesian posterior predictive  ... 
arXiv:1802.02626v3 fatcat:if2lkisjvfbw7memxldqfk2roq

On Interpolation Schemes for Nested Cartesian Finite Difference Grids of Different Size

Alejandro Figueroa, Rainald Lohner, Jay Sitaraman
2018 2018 AIAA Aerospace Sciences Meeting   unpublished
Nested cartesian grid systems by design require interpolation of solution fields from coarser to finer grid systems.  ...  Given this context, a series of interpolation algorithms for nested cartesian finite difference grids of different size were developed and tested.  ...  CONCLUSIONS AND OUTLOOK A series of interpolation algorithms for nested cartesian grids of different size were developed and tested.  ... 
doi:10.2514/6.2018-1561 fatcat:aqbcawbq6jgo3iibcaxhluxfqe
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