This paper introduces a propositional encoding of the recursive path order (RPO) on terms which is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. The proposed encoding allows us to use SAT solvers in order to determine whether a given term rewrite system is RPO terminating. An implementation is...

The present paper introduces an approach to construct lexicographic compositions of similarity-based fuzzy orderings. This construction is demonstrated by means of non-trivial examples. As this is a crucial feature of lexicographic composition, the preservation of linearity is studied in detail. We obtain once again that it is essential for meaningful results that the t-norm under consideration...

We generalize the main result of [K–K–S] concerning the convex embeddings of a chain Γ in a lexicographic power ∆Γ. For a fixed non-empty chain ∆, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functional equations (∆) ≃ Γ , (∆) ≃ Γ and (∆) ≃ Γ .

A small but notoriously hard integer program formulated by Donald Knuth fifty years ago is solved by three versions of a lexicographic algorithm using Gomory cuts. The lexicographic cutting plane algorithms are faster than CPLEX on this problem by a factor of at least 20.

We relate Kamin and Lévy’s original presentation of lexicographic path orders (LPO), using an inductive definition, to a presentation, which we will refer to as iterative lexicographic path orders (ILPO), based on Bergstra and Klop’s definition of recursive path orders by way of an auxiliary term rewriting sytem. Dedicated to Joseph Goguen, in celebration of his 65th birthday.

The aim of this work is to analyze lexicographic equilibrium problems on a topological Hausdorff vector space X, and their relationship with some other vector equilibrium problems. Existence results for the tangled lexicographic problem are proved via the study of a related sequential problem. This approach was already followed by the same authors in the case of variational inequalities.

given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...