141 research outputs found
More on Graph Rewriting With Contextual Refinement
In GRGEN , a graph rewrite generator tool, rules have the outstandingfeature that variables in their pattern and replacement graphs may be refined withmeta-rules based on contextual hyperedge replacement grammars. A refined rule maydelete, copy, and transform subgraphs of unbounded size and of variable shape. Inthis paper, we show that rules with contextual refinement can be transformed to stan-dard graph rewrite rules that perform the refinement incrementally, and are appliedaccording to a strategy called residual rewriting. With this transformation, it is possi-ble to state precisely whether refinements can be determined in finitely many steps ornot, and whether refinements are unique for every form of refined pattern or not
Defining Models - Meta Models versus Graph Grammars
The precise specification of software models is a major concern in model-driven design of object-oriented software. Metamodelling and graph grammars are apparent choices for such specifications. Metamodelling has several advantages: it is easy to use, and provides procedures that check automatically whether a model is valid or not. However, it is less suited for proving properties of models, or for generating large sets of example models. Graph grammars, in contrast, offer a natural procedure - the derivation process - for generating example models, and they support proofs because they define a graph language inductively. However, not all graph grammars that allow to specify practically relevant models are easily parseable. In this paper, we propose contextual star grammars as a graph grammar approach that allows for simple parsing and that is powerful enough for specifying non-trivial software models. This is demonstrated by defining program graphs, a language-independent model of object-oriented programs, with a focus on shape (static structure) rather than behavior
Graph Rewriting with Contextual Refinement
In the standard theory of graph transformation, a rule modifies only subgraphs of constant size and fixed shape. The rules supported by the graph-rewriting tool GrGen are far more expressive: they may modify subgraphs of unbounded size and variable shape. Therefore properties like termination and confluence cannot be analyzed as for the standard case. In order to lift such results, we formalize the outstanding feature of GrGen rules by using plain rules on two levels: schemata} are rules with variables; they are refined with meta-rules, which are based on contextual hyperedge replacement, before they are used for rewriting.We show that every rule based on single pushouts, on neighborhood-controlled embedding, or on variable substitution can be modeled by a schema with appropriate meta-rules. It turns out that the question whether schemata may have overlapping refinements is not decidable
Generating Semantic Graph Corpora with Graph Expansion Grammar
We introduce Lovelace, a tool for creating corpora of semantic graphs. The
system uses graph expansion grammar as a representational language, thus
allowing users to craft a grammar that describes a corpus with desired
properties. When given such grammar as input, the system generates a set of
output graphs that are well-formed according to the grammar, i.e., a graph
bank. The generation process can be controlled via a number of configurable
parameters that allow the user to, for example, specify a range of desired
output graph sizes. Central use cases are the creation of synthetic data to
augment existing corpora, and as a pedagogical tool for teaching formal
language theory.Comment: In Proceedings NCMA 2023, arXiv:2309.0733
Equivariant Hypergraph Diffusion Neural Operators
Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs
provide a promising way to model higher-order relations in data and further
solve relevant prediction tasks built upon such higher-order relations.
However, higher-order relations in practice contain complex patterns and are
often highly irregular. So, it is often challenging to design an HNN that
suffices to express those relations while keeping computational efficiency.
Inspired by hypergraph diffusion algorithms, this work proposes a new HNN
architecture named ED-HNN, which provably represents any continuous equivariant
hypergraph diffusion operators that can model a wide range of higher-order
relations. ED-HNN can be implemented efficiently by combining star expansions
of hypergraphs with standard message passing neural networks. ED-HNN further
shows great superiority in processing heterophilic hypergraphs and constructing
deep models. We evaluate ED-HNN for node classification on nine real-world
hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these
nine datasets and achieves more than 2\% in prediction accuracy over
four datasets therein.Comment: Code: https://github.com/Graph-COM/ED-HN
Towards rule-based visual programming of generic visual systems
This paper illustrates how the diagram programming language DiaPlan can be
used to program visual systems. DiaPlan is a visual rule-based language that is
founded on the computational model of graph transformation. The language
supports object-oriented programming since its graphs are hierarchically
structured. Typing allows the shape of these graphs to be specified recursively
in order to increase program security. Thanks to its genericity, DiaPlan allows
to implement systems that represent and manipulate data in arbitrary diagram
notations. The environment for the language exploits the diagram editor
generator DiaGen for providing genericity, and for implementing its user
interface and type checker.Comment: 15 pages, 16 figures contribution to the First International Workshop
on Rule-Based Programming (RULE'2000), September 19, 2000, Montreal, Canad
Parsing of Adaptive Star Grammars
In a recent paper, adaptive star grammars have been proposed as an
extension of node and hyperedge replacement grammars. A
rule in an adaptive star grammar is actually a rule schema which, via the
so-called cloning operation, yields a potentially infinite number of
concrete rules. Adaptive star grammars are motivated by application areas
such as modeling and refactoring object-oriented programs, and they are more
powerful than node and hyperedge replacement grammars by this mechanism. It
has been shown that the membership problem is decidable for a reasonably
large subclass of adaptive star grammars, however no parser has been
proposed. This paper describes such a parser for this subclass motivated by
the well-known string parser by Cocke, Younger, and
Kasami
COSMICAH 2005: workshop on verification of COncurrent Systems with dynaMIC Allocated Heaps (a Satellite event of ICALP 2005) - Informal Proceedings
Lisboa Portugal, 10 July 200
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