Polynomial solutions of algebraic difference equations and homogeneous symmetric polynomials

This article addresses the problem of computing an upper bound of the degree d of a polynomial solution P(x) of an algebraic differ- ence equation of the form Gx)(P(x −τ1), . . . , P(x −τs) + G0(x) = 0 when such P(x) with the coefficients in a field K of character- istic zero exists and where G is a non-linear s-variable polynomial with coefficients in K[x] and G0 is a polynomial with coefficients in K. It will be shown that if G is a quadratic polynomial with constant coefficients then one can construct a countable family of polynomi- als fl(u0) such that if there exists a (minimal) index l0 with fl0(u0) being a non-zero polynomial, then the degree d is one of its roots or d ≤ l0, or d < deg(G0). Moreover, the existence of such l0 will be proven for K being the field of real numbers. These results are based on the properties of the modules generated by special fami- lies of homogeneous symmetric polynomials. A sufficient condition for the existence of a similar bound of the degree of a polynomial solution for an algebraic difference equation with G of arbitrary total degree and with variable coefficients will be proven as well

IDLaS-NL – A platform for running customized studies on individual differences in Dutch language skills via the internet

We introduce the Individual Differences in Language Skills (IDLaS-NL) web platform, which enables users to run studies on individual differences in Dutch language skills via the internet. IDLaS-NL consists of 35 behavioral tests, previously validated in participants aged between 18 and 30 years. The platform provides an intuitive graphical interface for users to select the tests they wish to include in their research, to divide these tests into different sessions and to determine their order. Moreover, for standardized administration the platform provides an application (an emulated browser) wherein the tests are run. Results can be retrieved by mouse click in the graphical interface and are provided as CSV-file output via email. Similarly, the graphical interface enables researchers to modify and delete their study configurations. IDLaS-NL is intended for researchers, clinicians, educators and in general anyone conducting fundamental research into language and general cognitive skills; it is not intended for diagnostic purposes. All platform services are free of charge. Here, we provide a description of its workings as well as instructions for using the platform. The IDLaS-NL platform can be accessed at www.mpi.nl/idlas-nl

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

Mobile resource guarantees (evaluation paper)

This paper summarises the main outcomes of the Mobile Resource Guarantees (MRG) project, which focused on a proof-carrying-code (PCC) infrastructure for resources to be applied to mobile code. MRG was a three year project funded by the EC under the FET proactive initiative on Global Computing. We give an overview of the projects\u2019 results, discuss the lessons learnt from it and introduce follow-up work in new projects that will build on these results

Static Inference of Polynomial Size--Aware Types

Contains fulltext : 36493.pdf (author's version ) (Open Access)20 p

Univariate Polynomial Solutions of Nonlinear Polynomial Recurrence Relations

Contains fulltext : 83727.pdf (preprint version ) (Open Access)35 p

A higher-order size system for a higher-order functional language,Size Calculus for a Higher-Order Functional Language

Contains fulltext : 103399.pdf (preprint version ) (Open Access

A Size-Aware Type System with Algebraic Data Types

Contains fulltext : 72731.pdf (publisher's version ) (Open Access)34 p. p

Interpolation-based height analysis for improving a recrurrence solver

Contains fulltext : 91949.pdf (preprint version ) (Open Access)2th International Workshop on Foundational and Practical Aspects of Resource Analysis (FOPARA2011). Madrid, Spai