3,448 research outputs found
Towards Translating Graph Transformation Approaches by Model Transformations
Recently, many researchers are working on semantics preserving model transformation. In the field of graph transformation one can think of translating graph grammars written in one approach to a behaviourally equivalent graph grammar in another approach. In this paper we translate graph grammars developed with the GROOVE tool to AGG graph grammars by first investigating the set of core graph transformation concepts supported by both tools. Then, we define what it means for two graph grammars to be behaviourally equivalent, and for the regarded approaches we actually show how to handle different definitions of both - application conditions and graph structures. The translation itself is explained by means of intuitive examples
Graph-Based Shape Analysis Beyond Context-Freeness
We develop a shape analysis for reasoning about relational properties of data
structures. Both the concrete and the abstract domain are represented by
hypergraphs. The analysis is parameterized by user-supplied indexed graph
grammars to guide concretization and abstraction. This novel extension of
context-free graph grammars is powerful enough to model complex data structures
such as balanced binary trees with parent pointers, while preserving most
desirable properties of context-free graph grammars. One strength of our
analysis is that no artifacts apart from grammars are required from the user;
it thus offers a high degree of automation. We implemented our analysis and
successfully applied it to various programs manipulating AVL trees,
(doubly-linked) lists, and combinations of both
Probabilistic regular graphs
Deterministic graph grammars generate regular graphs, that form a structural
extension of configuration graphs of pushdown systems. In this paper, we study
a probabilistic extension of regular graphs obtained by labelling the terminal
arcs of the graph grammars by probabilities. Stochastic properties of these
graphs are expressed using PCTL, a probabilistic extension of computation tree
logic. We present here an algorithm to perform approximate verification of PCTL
formulae. Moreover, we prove that the exact model-checking problem for PCTL on
probabilistic regular graphs is undecidable, unless restricting to qualitative
properties. Our results generalise those of EKM06, on probabilistic pushdown
automata, using similar methods combined with graph grammars techniques.Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory
Graph grammars extend the theory of formal languages in order to model
distributed parallelism in theoretical computer science. We show here that to
certain classes of context-free and context-sensitive graph grammars one can
associate a Lie algebra, whose structure is reminiscent of the insertion Lie
algebras of quantum field theory. We also show that the Feynman graphs of
quantum field theories are graph languages generated by a theory dependent
graph grammar.Comment: 19 pages, LaTeX, 3 jpeg figure
Event Structure Semantics for Dynamic Graph Grammars
Dynamic graph grammars (DGGs) are a reflexive extension of Graph Grammars that have been introduced to represent mobile reflexive systems and calculi at a convenient level of abstraction. Persistent graph grammars (PGGs) are a class of graph grammars that admits a fully satisfactory concurrent semantics thanks to the fact that all so-called asymmetric conflicts (between items that are read by some productions and consumed by other) are avoided. In this paper we introduce a slight variant of DGGs, called persistent dynamic graph grammars (PDGGs), that can be encoded in PGGs preserving concurrency. Finally, PDGGs are exploited to define a concurrent semantics for the Join calculus enriched with persistent messaging (if preferred, the latter can be naively seen as dynamic nets with read arcs)
Growing Graphs with Hyperedge Replacement Graph Grammars
Discovering the underlying structures present in large real world graphs is a
fundamental scientific problem. In this paper we show that a graph's clique
tree can be used to extract a hyperedge replacement grammar. If we store an
ordering from the extraction process, the extracted graph grammar is guaranteed
to generate an isomorphic copy of the original graph. Or, a stochastic
application of the graph grammar rules can be used to quickly create random
graphs. In experiments on large real world networks, we show that random
graphs, generated from extracted graph grammars, exhibit a wide range of
properties that are very similar to the original graphs. In addition to graph
properties like degree or eigenvector centrality, what a graph "looks like"
ultimately depends on small details in local graph substructures that are
difficult to define at a global level. We show that our generative graph model
is able to preserve these local substructures when generating new graphs and
performs well on new and difficult tests of model robustness.Comment: 18 pages, 19 figures, accepted to CIKM 2016 in Indianapolis, I
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
- ā¦