12,751 research outputs found
Net processes correspond to derivation processes in graph grammars
AbstractThe aim of this paper is to compare the running behaviour of Petri nets, given by firing sequences and processes, with derivations and derivation processes in graph grammars. In a first step, Petri nets are simulated by graph grammars so that each firing in a net corresponds exactly to a direct derivation in the simulating graph grammar. In a second step the non-sequential behaviour of nets described by net processes is related to the non-sequential behaviour of graph grammars given by derivation processes. a one-to-one correppondence can be established between the processes on a Petri net and the complete conflict-free processes in the graph grammar simulating the net. This adds a new piece of evidence substantiating the close relationship between net and graph grammar theory
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
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
KMS states on Quantum Grammars
We consider quantum (unitary) continuous time evolution of spins on a lattice
together with quantum evolution of the lattice itself. In physics such
evolution was discussed in connection with quantum gravity. It is also related
to what is called quantum circuits, one of the incarnations of a quantum
computer. We consider simpler models for which one can obtain exact
mathematical results. We prove existence of the dynamics in both Schroedinger
and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We
show (for high temperatures) that for each system where the lattice undergoes
quantum evolution, there is a natural scaling leading to a quantum spin system
on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page
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