The lex leader method for breaking symmetry in CSPs typically produces a large set of lexicographic ordering constraints. Several rules have been proposed to reduce such sets whilst preserving logical equivalence. These reduction rules are not generally confluent: they may reach more than one fixpoint, depending on the order of application. These fixpoints vary in size. Smaller sets of lex cons...

The Recursive Path Ordering (rpo) is a syntactic ordering on terms that has been widely used for proving termination of term-rewriting systems 7,20]. How to combine term-rewriting with ordered resolution and paramodulation is now well-understood and it has been successfully applied in many theorem-proving systems 11,16,21]. In this setting an ordering such as rpo is used both to orient rewrite ...

The paper is a theoretical study of a generalization of the lexicographic rule for combining ordering relations. We define the concept of priority operator: a priority operator maps a family of relations to a single relation which represents their lexicographic combination according to a certain priority on the family of relations. We present four kinds of results. We show that the lexicographi...

Let A be a finite, totally ordered alphabet, and let P be the lexicographic ordering on A*. Let X be a subset of A*. The language of minimal words of X is the subset of X composed of the lexicographically minimal word of X for each length: Min(X)=[x # X | \w # X, |w|=|x| O xPw]. The aim of this paper is to prove that if L is a context-free language, then the language Min(L) context-free. ] 1997

This paper introduces an algorithm for determining data clusters called TILO/PRC (Topologically Intrinsic Lexicographic Ordering/Pinch Ratio Clustering). The theoretical foundation for this algorithm, developed in [14], uses ideas from topology (particularly knot theory) suggesting that it should be very flexible and robust with respect to noise. The TILO portion of the algorithm progressively ...

Fuzzy orderings with reference to an underlying context of similarity were first defined by Höhle and Blanchard [9]. Since then, several authors have contributed to the development of this class of fuzzy relations, both from the theoretical and the practical side (e.g. [1–4, 7, 8]). Two problems remained open throughout several years: how to define strict fuzzy orderings and how to define lexic...

Programming languages theory is full of problems that reduce to proving the consistency of a logic, such as the normalization of typed lambda-calculi, the decidability of equality in type theory, equivalence testing of traces in security, etc. Although the principle of transfinite induction is routinely employed by logicians in proving such theorems, it is rarely used by programming languages r...

The locally-lexicographic symmetric successive overrelaxation algorithm (ll-SSOR) is the most eeective parallel preconditioner known for iterative solvers used in lattice gauge theory. After reviewing the basic properties of ll-SSOR, the focus of this contribution is put on its parallel aspects: the administrative overhead of the parallel implementation of ll-SSOR, which is due to many conditio...

Resolving conflicts between default rules is a major subtask in performing default reasoning. A declarative way of controlling the resolution of conflicts is to assign priorities to default rules, and to prevent conflict resolution in ways that violate the priorities. This work extends Reiter’s default logic with a priority mechanism that is based on lexicographic comparison. Given a default th...

Several ways used to rank countries with respect to medals won during Olympic Games are discussed. In particular, it is shown that the unofficial rank used by the Olympic Committee is the only rank that does not allow one to use a numerical counter for ranking – this rank uses the lexicographic ordering to rank countries: one gold medal is more precious than any number of silver medals and one ...