Characterizing Compressibility of Disjoint Subgraphs with NLC Grammars

We consider compression of a given set S of isomorphic and disjoint subgraphs of a graph G using node label controlled (NLC) graph grammars. Given S and G, we characterize whether or not there exists a NLC graph grammar consisting of exactly one rule such that (1) each of the subgraphs S in G are compressed (i.e., replaced by a nonterminal) in the (unique) initial graph I , and (2) the set of generated terminal graphs is the singleton {G}.acceptance rate: 39%status: publishe

Matrix Graph Grammars

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.Comment: 321 pages, 75 figures. This book has is publisehd by VDM verlag, ISBN 978-363921255

Connectionist learning of regular graph grammars

This paper presents a new connectionist approach to grammatical inference. Using only positive examples, the algorithm learns regular graph grammars, representing two-dimensional iterative structures drawn on a discrete Cartesian grid. This work is intended as a case study in connectionist symbol processing andgeometric concept formation. A grammar is represented by a self-configuring connectionist network that is analogous to a transition diagram except that it can deal with graph grammars as easily as string grammars. Learning starts with a trivial grammar, expressing nogrammatical knowledge, which is then refined, by a process of successive node splitting and merging, into a grammar adequate to describe the population of input patterns. In conclusion, I argue that the connectionist style of computation is, in some ways, better suited than sequential computation to the task of representing and manipulating recursive structures

Lambda-calculus and formal language theory

Formal and symbolic approaches have offered computer science many application fields. The rich and fruitful connection between logic, automata and algebra is one such approach. It has been used to model natural languages as well as in program verification. In the mathematics of language it is able to model phenomena ranging from syntax to phonology while in verification it gives model checking algorithms to a wide family of programs. This thesis extends this approach to simply typed lambda-calculus by providing a natural extension of recognizability to programs that are representable by simply typed terms. This notion is then applied to both the mathematics of language and program verification. In the case of the mathematics of language, it is used to generalize parsing algorithms and to propose high-level methods to describe languages. Concerning program verification, it is used to describe methods for verifying the behavioral properties of higher-order programs. In both cases, the link that is drawn between finite state methods and denotational semantics provide the means to mix powerful tools coming from the two worlds

On the inference of non-confluent NLC graph grammars

Grammar inference deals with determining (preferably simple) models/grammars consistent with a set of observations. There is a large body of research on grammar inference within the theory of formal languages. However, there is surprisingly little known on grammar inference for graph grammars. In this paper we take a further step in this direction and work within the framework of node label controlled (NLC) graph grammars. Specifically, we characterize, given a set of disjoint and isomorphic subgraphs of a graph G, whether or not there is a NLC graph grammar rule which can generate these subgraphs to obtain G. This generalizes previous results by assuming that the set of isomorphic subgraphs is disjoint instead of non-touching. This leads naturally to consider the more involved ''non-confluent'' graph grammar rules.status: publishe