Families of binary relations are important interpretations of regular expressions, and the equivalence of two regular expressions with respect to their relational interpretations is decidable: the problem reduces to the equality of the denoted regular languages. Putting together a few results from the literature, we first make explicit a generalisation of this reduction, for regular expressions...

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties edge-coloured graphs. A homomorphism from $G$ $H$ is a vertex-mapping that preserves adjacencies and edge-colours. consider property having fixed $H$. The question we are interested in is: given an $G$, can perform $k$ operations so resulting admits $H$? vertex-deletion, edge-deletion ...

This survey paper provides an introduction to signed graphs, focusing on coloring. We shall introduce the concept of signed graphs, a proper coloring, and basic properties, such as a balanced graph and switchings. We will examine the chromatic number for six special signed graphs, upper bound the chromatic number, and discuss practical applications of signed graphs.

We address a problem connected to the unfolding semantics of functional programming languages: give a useful characterization of those infinite λ-terms that are λletrec-expressible in the sense that they arise as infinite unfoldings of terms in λletrec, the λ-calculus with letrec. We provide two characterizations, using concepts we introduce for infinite λ-terms: regularity, strong regularity, ...

We show that the downward-closure of a Petri net language is effectively computable. This is mainly done by using the notions defined for showing decidability of the reachability problem of Petri nets. In particular, we rely on Lambert’s construction of marked graph transition sequences — special instances of coverability graphs that allow us to extract constructively the simple regular express...

Given any dag t representing a fully or partially compressed XML document, we present a method for evaluating any positive unary query expressed in terms of Core XPath axes, on t, without unfolding t into a tree. To each Core XPath query of a certain basic type, we associate a word automaton; these automata run on the graph of dependency between the non-terminals of the straightline regular tre...

Diagonally equipotent matrices are diagonally dominant matrices for which dominance is never strict in any coordinate. They appear e.g. as Laplacian matrices of signed graphs. We show in this paper that for this class of matrices it is possible to provide a complete characterization of the stability properties based only on the signs of the entries of the matrices.

Recently, Zhang et al. [6] obtained some lower bounds of the signed domination number of a graph. In this paper, we obtain some new lower bounds of the signed domination number of a graph which are sharper than those of them.

We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in the projective plane and the characterization of whirls is in terms of topological duality in the annulus.

We give a decomposition theorem for signed graphs whose frame matroids are binary and a decomposition theorem for signed graphs whose frame matroids are quaternary.