Related papers: Regular Grammars for Sets of Graphs of Tree-Width …
Bounded infinite graphs are defined on the basis of natural physical requirements. When specialized to trees this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two. We verify…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
For a well-studied family of domination-type problems, in bounded-treewidth graphs, we investigate whether it is possible to find faster algorithms. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a set $S$ of vertices such…
The emergence of a variety of graph-based meaning representations (MRs) has sparked an important conversation about how to adequately represent semantic structure. These MRs exhibit structural differences that reflect different theoretical…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
Word-representable graphs are a class of graphs that can be represented by words, where edges and non-edges are determined by the alternation of letters in those words. Several papers in the literature have explored the…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
The article defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, a FSA can be seen as a graph for which the notion of genus arises. At the same time, a FSA has a semantics via its…
We consider classes of arbitrary (finite or infinite) graphs of bounded shrub-depth, specifically the classes $\mathrm{TM}_r(d)$ of arbitrary graphs that have tree models of height $d$ and $r$ labels. We show that the graphs of…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of…
Sentence ordering aims at arranging a list of sentences in the correct order. Based on the observation that sentence order at different distances may rely on different types of information, we devise a new approach based on multi-granular…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
There is a long line of research in the literature dedicated to word-representable graphs, which generalize several important classes of graphs. However, not much is known about word-representability of split graphs, another important class…
Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths -- a result that shows a strong link between the properties of these graph classes considered from the…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous context-free grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as…