28 research outputs found
Strategic Port Graph Rewriting: An Interactive Modelling and Analysis Framework
We present strategic portgraph rewriting as a basis for the implementation of
visual modelling and analysis tools. The goal is to facilitate the
specification, analysis and simulation of complex systems, using port graphs. A
system is represented by an initial graph and a collection of graph rewriting
rules, together with a user-defined strategy to control the application of
rules. The strategy language includes constructs to deal with graph traversal
and management of rewriting positions in the graph. We give a small-step
operational semantics for the language, and describe its implementation in the
graph transformation and visualisation tool PORGY.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767
Data-Structure Rewriting
We tackle the problem of data-structure rewriting including pointer
redirections. We propose two basic rewrite steps: (i) Local Redirection and
Replacement steps the aim of which is redirecting specific pointers determined
by means of a pattern, as well as adding new information to an existing data ;
and (ii) Global Redirection steps which are aimed to redirect all pointers
targeting a node towards another one. We define these two rewriting steps
following the double pushout approach. We define first the category of graphs
we consider and then define rewrite rules as pairs of graph homomorphisms of
the form "L R". Unfortunately, inverse pushouts (complement pushouts)
are not unique in our setting and pushouts do not always exist. Therefore, we
define rewriting steps so that a rewrite rule can always be performed once a
matching is found
Generalised compositionality in graph transformation
We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph passing between components, meaning that components may “learn” and “forget” subgraphs through communication with other components. Secondly, composition is no longer binary; instead, it can be repeated for an arbitrary number of components
Basic Results for Two Types of High-Level Replacement Systems1 1Research partially supported by the European Community under TMR Network GETGRATS and the ESPRIT Working Group APPLIGRAPH.
AbstractThe general idea of high-level replacement systems is to generalize the concept of graph transformation systems and graph grammars from graphs to all kinds of structures which are of interest in Computer Science and Mathematics. Within the algebraic approach of graph transformation this is possible by replacing graphs, graph morphisms, and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a suitable category. Of special interest are categories for all kinds of labelled and typed graphs, hypergraphs, algebraic specifications and Petri nets. In this paper, we review the basic results for high-level replacement systems in the algebraic double-pushout approach in the symmetric case, where both rule morphisms belong to a distinguished class
M
. Moreover we present for the first time the asymmetric type of high-level replacement systems, where only the left rule morphism
K
→
L
belongs to
M
A new graphical calculus of proofs
We offer a simple graphical representation for proofs of intuitionistic
logic, which is inspired by proof nets and interaction nets (two formalisms
originating in linear logic). This graphical calculus of proofs inherits good
features from each, but is not constrained by them. By the Curry-Howard
isomorphism, the representation applies equally to the lambda calculus,
offering an alternative diagrammatic representation of functional computations.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226
On Term-Graph Rewrite Strategies
AbstractWe tackle the problem of cyclic term-graph rewriting. We first revisit the classical algorithmic approach to term-graph rewriting by providing a definition of rewrite rules of the form lhs→rhs where the left-hand sides are term-graphs and the right-hand sides are sequences of actions. Such actions, which specify how to rewrite a term-graph in a stepwise manner, contribute to simplify substantially the definition of cyclic term-graph rewriting. Then we define a new class of term-graph rewrite systems which are confluent over the so-called admissible term-graphs. Finally, we provide an efficient rewrite strategy which contracts only needed redexes and give pointers to other results regarding optimal rewrite strategies of admissible term-graphs
A PBPO+ Graph Rewriting Tutorial
We provide a tutorial introduction to the algebraic graph rewriting formalism
PBPO+. We show how PBPO+ can be obtained by composing a few simple building
blocks, and model the reduction rules for binary decision diagrams as an
example. Along the way, we comment on how alternative design decisions lead to
related formalisms in the literature, such as DPO. We close with a detailed
comparison with Bauderon's double pullback approach.Comment: In Proceedings TERMGRAPH 2022, arXiv:2303.1421
Adhesive DPO Parallelism for Monic Matches
AbstractThis paper presents indispensable technical results of a general theory that will allow to systematically derive from a given reduction system a behavioral congruence that respects concurrency. The theory is developed in the setting of adhesive categories and is based on the work by Ehrig and König on borrowed contexts; the latter are an instance of relative pushouts, which have been proposed by Leifer and Milner. In order to lift the concurrency theory of dpo rewriting to borrowed contexts we will study the special case of dpo rewriting with monic matches in adhesive categories: more specifically we provide a generalized Butterfly Lemma together with a Local Church Rosser and Parallelism theorem