Consider a polynomial F in m variables and a finite point ensemble S = S1 × · · · × Sm. When given the leading monomial of F with respect to a lexicographic ordering we derive improved information on the possible number of zeros of F of multiplicity at least r from S. We then use this information to design a list decoding algorithm for a large class of affine variety codes.

The purpose of this article is to study the role of Gödel’s functional interpretation in the extraction of programs fromproofs inwell quasi-order theory. Themain focus is on the interpretation of Nash-Williams’ famous minimal bad sequence construction, and the exploration of a number of much broader problems which are related to this, particularly the question of the constructive meaning of Zor...

In 1991 I described a particularly simple and elegant watershed algorithm, where the ooding a topographic surface was scheduled by a hierarchical queue. In 2004 the watershed line has been described as the skeleton by zone of in uence for the topographic distance. The same algorithm still applies. In 2012 I de ned a new distance based on a lexicographic ordering of the downstream paths leading ...

We present simple techniques for deciding the satissability of lexicographic path ordering constraints under two diierent semantics: solutions built over the given signature and solutions in extended signatures. For both cases we give the rst NP algorithms, which is optimal as we prove the problems to be NP-complete. We discuss the eecient applicability of the techniques in practice, where, as ...

We claim that the reduction of Post's Correspondence Problem to the decision problem of a theory provides a useful tool for proving undecidability of rst order theories given by some interpretation. The goal of this paper is to deene a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associ...

This paper deals with qualitative evaluation processes when the worth of items is computed by means of Sugeno integral. One limitation of this approach is the coarse ranking of items it produces. In order to refine this ranking, generalizations of leximin and leximax to Sugeno integrals are studied. Numerical encodings of such generalized lexicographic methods are described by means of mappings...

This survey paper contains a description of some recent results concerning Sturmian and episturmian words, with particular emphasis on central words. We list fourteen characterizations of central words. We give the characterizations of Sturmian and episturmian words by lexicographic ordering, we show how the Burrows-Wheeler transform behaves on Sturmian words. We mention results on balanced epi...

In this article, we propose a multiple objective optimization based approach for the short term scheduling of batch plants to select superior solutions when compared to the single objective problem. Two alternate approaches to optimality, viz. lexicographic and pareto-optimality based formulations are considered here. We demonstrate the suitability of lexicographic optimization for the case whe...

Abstract This work aims at reviewing the state of art field lexicographic multi/many-objective optimization. The discussion starts with a review literature, emphasizing numerous application in real life and recent burst received by advent new computational frameworks which well such contexts, e.g., Grossone Methodology. Then focus shifts on class problems proposed studied for first time only re...

We analyze the autocorrelations for the Local Hybrid Monte Carlo algorithm [1] in the context of free field theory. In this case this is just Adler’s overrelaxation algorithm [2]. We consider the algorithm with even/odd, lexicographic, and random updates, and show that its efficiency depends crucially on this ordering of sites when optimized for a given class of operators. In particular, we sho...