16,870 research outputs found
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
Graph Interpolation Grammars as Context-Free Automata
A derivation step in a Graph Interpolation Grammar has the effect of scanning
an input token. This feature, which aims at emulating the incrementality of the
natural parser, restricts the formal power of GIGs. This contrasts with the
fact that the derivation mechanism involves a context-sensitive device similar
to tree adjunction in TAGs. The combined effect of input-driven derivation and
restricted context-sensitiveness would be conceivably unfortunate if it turned
out that Graph Interpolation Languages did not subsume Context Free Languages
while being partially context-sensitive. This report sets about examining
relations between CFGs and GIGs, and shows that GILs are a proper superclass of
CFLs. It also brings out a strong equivalence between CFGs and GIGs for the
class of CFLs. Thus, it lays the basis for meaningfully investigating the
amount of context-sensitiveness supported by GIGs, but leaves this
investigation for further research
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
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
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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
Equational reasoning with context-free families of string diagrams
String diagrams provide an intuitive language for expressing networks of
interacting processes graphically. A discrete representation of string
diagrams, called string graphs, allows for mechanised equational reasoning by
double-pushout rewriting. However, one often wishes to express not just single
equations, but entire families of equations between diagrams of arbitrary size.
To do this we define a class of context-free grammars, called B-ESG grammars,
that are suitable for defining entire families of string graphs, and crucially,
of string graph rewrite rules. We show that the language-membership and
match-enumeration problems are decidable for these grammars, and hence that
there is an algorithm for rewriting string graphs according to B-ESG rewrite
patterns. We also show that it is possible to reason at the level of grammars
by providing a simple method for transforming a grammar by string graph
rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The
final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-21145-9_
Search and Result Presentation in Scientific Workflow Repositories
We study the problem of searching a repository of complex hierarchical
workflows whose component modules, both composite and atomic, have been
annotated with keywords. Since keyword search does not use the graph structure
of a workflow, we develop a model of workflows using context-free bag grammars.
We then give efficient polynomial-time algorithms that, given a workflow and a
keyword query, determine whether some execution of the workflow matches the
query. Based on these algorithms we develop a search and ranking solution that
efficiently retrieves the top-k grammars from a repository. Finally, we propose
a novel result presentation method for grammars matching a keyword query, based
on representative parse-trees. The effectiveness of our approach is validated
through an extensive experimental evaluation
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