10,461 research outputs found
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
Introducing the Concept of Activation and Blocking of Rules in the General Framework for Regulated Rewriting in Sequential Grammars
We introduce new possibilities to control the application of rules based on
the preceding application of rules which can be de ned for a general model of sequential
grammars and we show some similarities to other control mechanisms as graph-controlled
grammars and matrix grammars with and without applicability checking as well as gram-
mars with random context conditions and ordered grammars. Using both activation and
blocking of rules, in the string and in the multiset case we can show computational com-
pleteness of context-free grammars equipped with the control mechanism of activation
and blocking of rules even when using only two nonterminal symbols
A Reformulation of Matrix Graph Grammars with Boolean Complexes
Prior publication in the Electronic Journal of Combinatorics.Graph transformation is concerned with the manipulation of graphs by means of rules. Graph grammars have been traditionally studied using techniques from category theory. In previous works, we introduced Matrix Graph Grammars (MGG) as a purely algebraic approach for the study of graph dynamics, based on the representation of simple graphs by means of their adjacency matrices.
The observation that, in addition to positive information, a rule implicitly defines negative conditions for its application (edges cannot become dangling, and cannot be added twice as we work with simple digraphs) has led to a representation of graphs as two matrices encoding positive and negative information. Using this representation, we have reformulated the main concepts in MGGs, while we have introduced other new ideas. In particular, we present (i) a new formulation of productions together with an abstraction of them (so called swaps), (ii) the notion of coherence, which checks whether a production sequence can be potentially applied, (iii) the minimal graph enabling the applicability of a sequence, and (iv) the conditions for compatibility of sequences (lack of dangling edges) and G-congruence (whether two sequences have the same minimal initial graph).This work has been partially sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN)
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Context-free grammars with graph control
Context-free grammars with graph control provide a general framework for the various types of context-free grammars with regulated rewriting. The vertices or edges of the directed graph are labeled with the productions of the grammar. The only strings in the language generated by the grammar are those whose derivations correspond to labeled paths in the graph. Inclusion relations among the various classes of context-free grammars with regulated rewriting such as programmed grammars (without failure fields), matrix grammars, periodically time-variant grammars, state grammars, and grammars with regular control are easily obtained and the graph provides insight into the nature of the restriction. Adding negative context to context-free grammars with graph control, we obtain a class of grammars equivalent to the context-free programmed grammars
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
Context-Free Path Querying by Matrix Multiplication
Graph data models are widely used in many areas, for example, bioinformatics,
graph databases. In these areas, it is often required to process queries for
large graphs. Some of the most common graph queries are navigational queries.
The result of query evaluation is a set of implicit relations between nodes of
the graph, i.e. paths in the graph. A natural way to specify these relations is
by specifying paths using formal grammars over the alphabet of edge labels. An
answer to a context-free path query in this approach is usually a set of
triples (A, m, n) such that there is a path from the node m to the node n,
whose labeling is derived from a non-terminal A of the given context-free
grammar. This type of queries is evaluated using the relational query
semantics. Another example of path query semantics is the single-path query
semantics which requires presenting a single path from the node m to the node
n, whose labeling is derived from a non-terminal A for all triples (A, m, n)
evaluated using the relational query semantics. There is a number of algorithms
for query evaluation which use these semantics but all of them perform poorly
on large graphs. One of the most common technique for efficient big data
processing is the use of a graphics processing unit (GPU) to perform
computations, but these algorithms do not allow to use this technique
efficiently. In this paper, we show how the context-free path query evaluation
using these query semantics can be reduced to the calculation of the matrix
transitive closure. Also, we propose an algorithm for context-free path query
evaluation which uses relational query semantics and is based on matrix
operations that make it possible to speed up computations by using a GPU.Comment: 9 pages, 11 figures, 2 table
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