We present a new precedence-based termination ordering for (polymorphic) higher-order terms without-abstraction. The ordering has been designed to strictly generalize the lexicographic path ordering (on rst-order terms). It is relatively simple, but can be used to prove termination of many higher-order rewrite systems, especially those corresponding to typical functional programs. We establish ...

There is a variety of methods for ranking objectives in multiobjective optimization and some are difficult to define because they require information a priori (e.g. establishing weights in a weighted approach or setting the ordering in a lexicographic approach). In manyobjective optimization problems, those methods may exhibit poor diversification and intensification performance. We propose the...

We prove that there exists no algorithm to decide whether the language generated by a context-free grammar is dense with respect to the lexicographic ordering. As a corollary to this result, we show that it is undecidable whether the lexicographic orderings of the languages generated by two context-free grammars have the same order type.

We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show that decomposing such constraints carries a penalty either in the amount or the cost of constraint propagation. We therefore present a global consistency algorithm which enforces a lex...

Motivation The minimizers scheme is a method for selecting k -mers from sequences. It is used in many bioinformatics software tools to bin comparable sequences or to sample a sequence in a deterministic fashion at approximately regular intervals, in order to reduce memory consumption and processing time. Although very useful, the minimizers selection procedure has undesirable behaviors (e.g. to...

An ordering for terms with sequence variables and flexible arity symbols is presented. The ordering coincides with the lexicographic extension of multiset path ordering on terms without sequence variables. It is shown that the classical strict superposition calculus with ordering and equality constraints can be used as a refutationally complete proving method for well-constrained sets of clause...

We show that it is decidable in exponential time whether the lexicographic ordering of a context-free language is scattered, or a wellordering.

We introduce a new global constraint which combines together a lexicographic ordering constraint with some sum constraints. Applications for this constraint include balanced incomplete block designs and the ternary Steiner problem. We develop an efficient linear time algorithm for propagating this constraint. This combination of constraints increases the filtering, leading to significant decrea...

We show that every additively representable comparative probability ordering is determined by at least n− 1 binary subset comparisons. We show that there are many orderings of this kind, not just the lexicographic ordering. These results provide answers to two questions asked by Fishburn.

We prove that the finite condensation rank (FC-rank) of the lexicographic ordering of a context-free language is strictly less than ω.