Related papers: On the Completeness of Interpolation Algorithms
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
The interpolation-based decoding that was developed for general evaluation AG codes is shown to be equally applicable to general differential AG codes. A performance analysis of the decoding algorithm, which is parallel to that of its…
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets…
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain…
We study the Lyndon interpolation property (LIP) and the uniform Lyndon interpolation property (ULIP) for extensions of $\mathbf{S4}$ and intermediate propositional logics. We prove that among the 18 consistent normal modal logics of finite…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
Let $A_p(\C)$ be the space of entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$ and let $V$ be a discrete sequence of complex numbers which is not a uniqueness set for $A_p(\C)$. We use $L^2$ estimates for the…
Program synthesis is the task of automatically deriving a program that has been specified by a user in advance. Combining automated theorem proving with program synthesis enables the automated construction of proven-to-be-correct programs,…
We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap…
In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin.…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…
We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory