14,709 research outputs found
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_
Context-Free Path Querying with Structural Representation of Result
Graph data model and graph databases are very popular in various areas such
as bioinformatics, semantic web, and social networks. One specific problem in
the area is a path querying with constraints formulated in terms of formal
grammars. The query in this approach is written as grammar, and paths querying
is graph parsing with respect to given grammar. There are several solutions to
it, but how to provide structural representation of query result which is
practical for answer processing and debugging is still an open problem. In this
paper we propose a graph parsing technique which allows one to build such
representation with respect to given grammar in polynomial time and space for
arbitrary context-free grammar and graph. Proposed algorithm is based on
generalized LL parsing algorithm, while previous solutions are based mostly on
CYK or Earley algorithms, which reduces time complexity in some cases.Comment: Evaluation extende
Nested Term Graphs (Work In Progress)
We report on work in progress on 'nested term graphs' for formalizing
higher-order terms (e.g. finite or infinite lambda-terms), including those
expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea
is to represent the nested scope structure of a higher-order term by a nested
structure of term graphs.
Based on a signature that is partitioned into atomic and nested function
symbols, we define nested term graphs both in a functional representation, as
tree-like recursive graph specifications that associate nested symbols with
usual term graphs, and in a structural representation, as enriched term graph
structures. These definitions induce corresponding notions of bisimulation
between nested term graphs. Our main result states that nested term graphs can
be implemented faithfully by first-order term graphs.
keywords: higher-order term graphs, context-free grammars, cyclic
lambda-terms, higher-order rewrite systemsComment: In Proceedings TERMGRAPH 2014, arXiv:1505.0681
Network Analysis with Stochastic Grammars
Digital forensics requires significant manual effort to identify items of evidentiary interest from the ever-increasing volume of data in modern computing systems. One of the tasks digital forensic examiners conduct is mentally extracting and constructing insights from unstructured sequences of events. This research assists examiners with the association and individualization analysis processes that make up this task with the development of a Stochastic Context -Free Grammars (SCFG) knowledge representation for digital forensics analysis of computer network traffic. SCFG is leveraged to provide context to the low-level data collected as evidence and to build behavior profiles. Upon discovering patterns, the analyst can begin the association or individualization process to answer criminal investigative questions. Three contributions resulted from this research. First , domain characteristics suitable for SCFG representation were identified and a step -by- step approach to adapt SCFG to novel domains was developed. Second, a novel iterative graph-based method of identifying similarities in context-free grammars was developed to compare behavior patterns represented as grammars. Finally, the SCFG capabilities were demonstrated in performing association and individualization in reducing the suspect pool and reducing the volume of evidence to examine in a computer network traffic analysis use case
Confluent Orthogonal Drawings of Syntax Diagrams
We provide a pipeline for generating syntax diagrams (also called railroad
diagrams) from context free grammars. Syntax diagrams are a graphical
representation of a context free language, which we formalize abstractly as a
set of mutually recursive nondeterministic finite automata and draw by
combining elements from the confluent drawing, layered drawing, and smooth
orthogonal drawing styles. Within our pipeline we introduce several heuristics
that modify the grammar but preserve the language, improving the aesthetics of
the final drawing.Comment: GD 201
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
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
- …