96 research outputs found
Boundary graph grammars with dynamic edge relabeling
AbstractMost NLC-like graph grammars generate node-labeled graphs. As one of the exceptions, eNCE graph grammars generate graphs with edge labels as well. We investigate this type of graph grammar and show that the use of edge labels (together with the NCE feature) is responsible for some new properties. Especially boundary eNCE (B-eNCE) grammars are considered. First, although eNCE grammars have the context-sensitive feature of “blocking edges,” we show that B-eNCE grammars do not. Second, we show the existence of a Chomsky normal form and a Greibach normal form for B-eNCE grammars. Third, the boundary eNCE languages are characterized in terms of regular tree and string languages. Fourth, we prove that the class of (boundary) eNCE languages properly contains the closure of the class of (boundary) NLC languages under node relabelings. Analogous results are shown for linear eNCE grammars
Symbol–Relation Grammars: A Formalism for Graphical Languages
AbstractA common approach to the formal description of pictorial and visual languages makes use of formal grammars and rewriting mechanisms. The present paper is concerned with the formalism of Symbol–Relation Grammars (SR grammars, for short). Each sentence in an SR language is composed of a set of symbol occurrences representing visual elementary objects, which are related through a set of binary relational items. The main feature of SR grammars is the uniform way they use context-free productions to rewrite symbol occurrences as well as relation items. The clearness and uniformity of the derivation process for SR grammars allow the extension of well-established techniques of syntactic and semantic analysis to the case of SR grammars. The paper provides an accurate analysis of the derivation mechanism and the expressive power of the SR formalism. This is necessary to fully exploit the capabilities of the model. The most meaningful features of SR grammars as well as their generative power are compared with those of well-known graph grammar families. In spite of their structural simplicity, variations of SR grammars have a generative power comparable with that of expressive classes of graph grammars, such as the edNCE and the N-edNCE classes
Graph Transformations and Game Theory: A Generative Mechanism for Network Formation
Many systems can be described in terms of networks with characteristic structural properties. To better understand the formation and the dynamics of complex networks one can develop generative models. We propose here a generative model (named dynamic spatial game) that combines graph transformations and game theory. The idea is that a complex network is obtained by a sequence of node-based transformations determined by the interactions of nodes present in the network. We model the node-based transformations by using graph grammars and the interactions between the nodes by using game theory. We illustrate dynamic spatial games on a couple of examples: the role of cooperation in tissue formation and tumor development and the emergence of patterns during the formation of ecological networks
Decision problems for node label controlled graph grammars
AbstractTwo basic techniques are presented to show the decidability status of a number of problems concerning node label controlled graph grammars. Most of the problems are of graph-theoretic nature and concern topics like planarity, connectedness and bounded degreeness of graph languages
Shrub-depth: Capturing Height of Dense Graphs
The recent increase of interest in the graph invariant called tree-depth and
in its applications in algorithms and logic on graphs led to a natural
question: is there an analogously useful "depth" notion also for dense graphs
(say; one which is stable under graph complementation)? To this end, in a 2012
conference paper, a new notion of shrub-depth has been introduced, such that it
is related to the established notion of clique-width in a similar way as
tree-depth is related to tree-width. Since then shrub-depth has been
successfully used in several research papers. Here we provide an in-depth
review of the definition and basic properties of shrub-depth, and we focus on
its logical aspects which turned out to be most useful. In particular, we use
shrub-depth to give a characterization of the lower levels of the
MSO1 transduction hierarchy of simple graphs
Design, construction, and application of a generic visual language generation environment
2000-2001 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe
On the expressive power of permanents and perfect matchings of matrices of bounded pathwidth/cliquewidth
Some 25 years ago Valiant introduced an algebraic model of computation in
order to study the complexity of evaluating families of polynomials. The theory
was introduced along with the complexity classes VP and VNP which are analogues
of the classical classes P and NP. Families of polynomials that are difficult
to evaluate (that is, VNP-complete) includes the permanent and hamiltonian
polynomials. In a previous paper the authors together with P. Koiran studied
the expressive power of permanent and hamiltonian polynomials of matrices of
bounded treewidth, as well as the expressive power of perfect matchings of
planar graphs. It was established that the permanent and hamiltonian
polynomials of matrices of bounded treewidth are equivalent to arithmetic
formulas. Also, the sum of weights of perfect matchings of planar graphs was
shown to be equivalent to (weakly) skew circuits. In this paper we continue the
research in the direction described above, and study the expressive power of
permanents, hamiltonians and perfect matchings of matrices that have bounded
pathwidth or bounded cliquewidth. In particular, we prove that permanents,
hamiltonians and perfect matchings of matrices that have bounded pathwidth
express exactly arithmetic formulas. This is an improvement of our previous
result for matrices of bounded treewidth. Also, for matrices of bounded
weighted cliquewidth we show membership in VP for these polynomials.Comment: 21 page
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