249,940 research outputs found
Graph Rewriting and Relabeling with PBPO+
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting
with strong matching. Our approach, called \pbpostrong, exerts more control
over the embedding of the pattern in the host graph, which is important for a
large class of graph rewrite systems. In addition, we show that \pbpostrong is
well-suited for rewriting labeled graphs and certain classes of attributed
graphs. For this purpose, we employ a lattice structure on the label set and
use order-preserving graph morphisms. We argue that our approach is simpler and
more general than related relabeling approaches in the literature.Comment: 20 pages, accepted to the International Conference on Graph
Transformation 2021 (ICGT 2021
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_
Graph Transformation for Domain-Specific Discrete Event Time Simulation
Proceedings of: Fifth International Conference on Graph Transformation (ICGT 2010). Enschede, The Netherlands, September 27–October 2, 2010.Graph transformation is being increasingly used to express the semantics of domain specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time in order to represent accurately the behaviour of the real system and to obtain useful simulation metrics. Inspired by the vast knowledge and experience accumulated by the discrete event simulation community, we propose a novel way of adding explicit time to graph transformation rules. In particular, we take the event scheduling discrete simulation world view and incorporate to the rules the ability of scheduling the occurrence of other rules in the future. Hence, our work combines standard, efficient techniques for discrete event simulation (based on the handling of a future event set) and the intuitive, visual nature of graph transformation. Moreover, we show how our formalism can be used to give semantics to other timed approaches.Work partially sponsored by the Spanish Ministry of Science and Innovation, under project “METEORIC” (TIN2008-02081) and mobility grants JC2009-00015 and PR2009-0019, as well as by the R&D programme of the Community of Madrid, project “e-Madrid” (S2009/TIC-1650).Publicad
Incorrectness Logic for Graph Programs
Program logics typically reason about an over-approximation of program
behaviour to prove the absence of bugs. Recently, program logics have been
proposed that instead prove the presence of bugs by means of under-approximate
reasoning, which has the promise of better scalability. In this paper, we
present an under-approximate program logic for a nondeterministic graph
programming language, and show how it can be used to reason deductively about
program incorrectness, whether defined by the presence of forbidden graph
structure or by finitely failing executions. We prove this incorrectness logic
to be sound and complete, and speculate on some possible future applications of
it.Comment: Accepted by the 14th International Conference on Graph Transformation
(ICGT 2021
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