We introduce syntactic restrictions of the lexicographic path ordering to obtain the Light Lexicographic Path Ordering. We show that the light lexicographic path ordering leads to a characterisation of the functions computable in space bounded by a polynomial in the size of the inputs.

The words of a context-free language, ordered by the lexicographic ordering, form a context-free linear ordering. It is well-known that the linear orderings associated with deterministic context-free languages have a decidable monadic second-order theory. In stark contrast, we give an example of a context-free language whose lexicographic ordering has an undecidable first-order theory.

This paper introduces six ways for handling a chain of lexicographic ordering constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a chain of lexicographic ordering constraint within a generic geometric constraint kernel, the four latter ...

Received Revised ABSTRACT We show how to solve boolean combinations of inequations s > t in the Herbrand Universe, assuming that is interpreted as a lexicographic path ordering extending a total precedence. In other words, we prove that the existential fragment of the theory of a lexicographic path ordering which extends a total precedence is decidable.

Location problems with Q (in general connicting) criteria are considered. After reviewing previous results of the authors dealing with lexicographic and Pareto location the main focus of the paper is on max-ordering locations. In these location problems the worst of the single objectives is minimized. After discussing some general results (including reductions to single criterion problems and t...

Geometric lattices are characterized as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. Equivalently, geometric lattices are shown to be exactly those finite lattices such that every ordering on the join-irreducibles induces a lexicographic shelling. This new characterization fits into a similar ...

 Lexicographic ordering by spectral moments ($S$-order) among all trees is discussed in this‎ ‎paper‎. ‎For two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{T}_n^{p‎, ‎q}={T‎: ‎T$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. Furthermore, ‎the last four trees‎, ‎in the $S$-order‎, ‎among $mathscr{T}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

We introduce a new global constraint which combines together the lexicographic ordering constraint with some sum constraints. Lexicographic ordering constraints are frequently used to break symmetry, whilst sum constraints occur in many problems involving capacity or partitioning. Our results show that this global constraint is useful when there is a very large space to explore, such as when th...

It is shown that a termination proof for a term rewriting system using a lexicographic path ordering yields a multiply recursive bound on the length of derivations, measured in the depth of the starting term. This result is essentially optimal since for every multiply recursive function f a rewrite system (which reduces under the lexicographic path ordering) can be found such that its derivatio...