## A Rewriting Calculus for Multigraphs with Ports (2007)

Venue: | In Proc. of RULE’07 |

Citations: | 7 - 6 self |

### BibTeX

@INPROCEEDINGS{Andrei07arewriting,

author = {Oana Andrei and Hélène Kirchner},

title = {A Rewriting Calculus for Multigraphs with Ports},

booktitle = {In Proc. of RULE’07},

year = {2007}

}

### OpenURL

### Abstract

In this paper, we define labeled multigraphs with ports, a graph model which specifies connection points for nodes and allows multiple edges and loops. The dynamic evolution of these structures is expressed with multigraph rewrite rules and a multigraph rewriting relation. Then we encode the multigraphs and multigraph rewriting using algebraic terms and term rewriting to provide an operational semantics of the multigraph rewriting relation. This term version can be embedded in the rewriting calculus, thus defining for labeled multigraph transformations a high-level pattern calculus, called ρmg-calculus. Keywords: multigraphs with ports, multigraph rewriting, term rewriting, rewriting calculus 1

### Citations

952 |
Term Rewriting and All That
- Baader, Nipkow
- 1998
(Show Context)
Citation Context ...briefly review some basic definitions of graph theory and graph transformation [12,18] used in this paper. We adopt the classical definitions for order-sorted algebra and term rewriting from [14] and =-=[4,15]-=- respectively. Labeled Graphs. A label alphabet L =(LV, LE) is a pair of sets of node labels and edge labels. A (finite) graph over L is a triple G =(V, E, s, t, l) where V is a set {v1, . . . , vk} o... |

206 | Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations
- Goguen, Meseguer
- 1992
(Show Context)
Citation Context ...ction we briefly review some basic definitions of graph theory and graph transformation [12,18] used in this paper. We adopt the classical definitions for order-sorted algebra and term rewriting from =-=[14]-=- and [4,15] respectively. Labeled Graphs. A label alphabet L =(LV, LE) is a pair of sets of node labels and edge labels. A (finite) graph over L is a triple G =(V, E, s, t, l) where V is a set {v1, . ... |

132 | Core formal molecular biology
- Danos, Laneve
(Show Context)
Citation Context ...s in nodes for partitioning incidences. An immediate application of multigraphs with ports is for modeling protein-protein interactions concerned with the connectivity inside molecular complexes (see =-=[13]-=- for a process algebra approach, and [7] for an approach based on graph rewriting). Proteins are abstracted as boxes with interaction sites on the surface having particular states. Hence, adding a ref... |

96 | Algebraic approaches to graph transformation. Part I: Basic concepts and double pushout approach
- Corradini, Montanari, et al.
(Show Context)
Citation Context ...igraphs with ports. The proofs of the results stated in this paper are available in [2]. 2 Background In this section we briefly review some basic definitions of graph theory and graph transformation =-=[12,18]-=- used in this paper. We adopt the classical definitions for order-sorted algebra and term rewriting from [14] and [4,15] respectively. Labeled Graphs. A label alphabet L =(LV, LE) is a pair of sets of... |

64 | The rewriting calculus
- Cirstea, Kirchner
- 2001
(Show Context)
Citation Context ...ρ-calculus), the embedding of mg-rewriting in the rewriting calculus is presented, resulting in a multigraph term rewriting calculus. 5.1 The Rewriting Calculus The rewriting calculus (or ρ-calculus) =-=[10]-=- extends first-order term rewriting and λ-calculus. From the λ-calculus, the ρ-calculus inherits its higher-order capabilities and the explicit treatment of functions and their applications. It was in... |

63 | 2001): Bigraphical Reactive Systems - Milner |

38 | Tom: piggybacking rewriting on java
- Balland, Brauner, et al.
- 2007
(Show Context)
Citation Context ... for labeled multigraphs with ports, which is an instance of ρ-calculus, and we call it the ρmg-calculus. 6 Conclusion An implementation for the multigraphs with ports is currently developed in TOM 1 =-=[6]-=- using pointers for the termgraph implementation [5] which handles cyclic termgraphs as well. We use a more efficient encoding for programming by representing a multigraph by its node set and each edg... |

37 | Programmed Graph Replacement Systems
- Schürr
- 1997
(Show Context)
Citation Context ...ormation provides a rule-based modeling of their dynamic evolution. Different approaches have been proposed to formalize graph transformation and to define graph rewriting, summarized for instance in =-=[18]-=-. We have explored graph models for simulating chemical reactors [8,1] and protein interactions [3]. In this context we found the need for graph structures where the nodes have points, called ports, f... |

30 | Promoting Rewriting to a Programming Language: A Compiler for NonDeterministic Rewrite Programs in Associative-Commutative Theories
- KIRCHNER, MOREAU
(Show Context)
Citation Context ...e rules with extension variables that help storing the context and applying rewrite steps in subterms. This is a usual method employed when performing rewriting modulo associativity and commutativity =-=[16]-=-. We usually denote by W an extension variable and by t the extension of term t. For each rewrite rule t1 ⇾ t2, extension variables are appended to set-sorted terms 9Andrei and Kirchner (Propagate) {... |

21 |
W.: Graph theory for rule-based modeling of biochemical networks
- Blinov, Yang, et al.
- 2006
(Show Context)
Citation Context ...n immediate application of multigraphs with ports is for modeling protein-protein interactions concerned with the connectivity inside molecular complexes (see [13] for a process algebra approach, and =-=[7]-=- for an approach based on graph rewriting). Proteins are abstracted as boxes with interaction sites on the surface having particular states. Hence, adding a refinement on the ports and calling them si... |

18 | Rewrite strategies in the rewriting calculus
- Cirstea, Kirchner, et al.
- 2003
(Show Context)
Citation Context ...2) ≀ . . . with σi ∈Sol(p ≪ t3) (δ) (t1 ≀ t2)t3 →δ t1t3 ≀ t2t3 Fig. 11. The semantics of ρ-calculus An important feature of the ρ-calculus is its capability of encoding rewrite strategies as shown in =-=[11]-=-. The basic strategies are the rewrite rules. An immediate application of the use of rewrite strategies in the ρ-calculus is the encoding of conditional rewriting [10]. The ρ-calculus has been proved ... |

6 | Term-graph rewriting in tom using relative positions
- Balland, Brauner
(Show Context)
Citation Context ...tance of ρ-calculus, and we call it the ρmg-calculus. 6 Conclusion An implementation for the multigraphs with ports is currently developed in TOM 1 [6] using pointers for the termgraph implementation =-=[5]-=- which handles cyclic termgraphs as well. We use a more efficient encoding for programming by representing a multigraph by its node set and each edge by a pointer to the target port 1 Web page http://... |

4 |
Non-intrusive Formal Methods and Strategic Rewriting for a Chemical Application
- Andrei, Ibanescu, et al.
- 2006
(Show Context)
Citation Context ...ifferent approaches have been proposed to formalize graph transformation and to define graph rewriting, summarized for instance in [18]. We have explored graph models for simulating chemical reactors =-=[8,1]-=- and protein interactions [3]. In this context we found the need for graph structures where the nodes have points, called ports, for attaching the edges, thus providing an explicit partitioning of nod... |

1 |
A Rewriting Calculus for Labeled Multigraphs with Ports, Long version available at http://hal.inria.fr/inria-00139363/en
- Andrei, Kirchner
(Show Context)
Citation Context ...t. 6 we give some implementation hints for multigraph rewriting and sketch some extensions and applications for multigraphs with ports. The proofs of the results stated in this paper are available in =-=[2]-=-. 2 Background In this section we briefly review some basic definitions of graph theory and graph transformation [12,18] used in this paper. We adopt the classical definitions for order-sorted algebra... |

1 |
From Chemical Rules to Term
- Bournez, Ibanescu, et al.
(Show Context)
Citation Context ...ifferent approaches have been proposed to formalize graph transformation and to define graph rewriting, summarized for instance in [18]. We have explored graph models for simulating chemical reactors =-=[8,1]-=- and protein interactions [3]. In this context we found the need for graph structures where the nodes have points, called ports, for attaching the edges, thus providing an explicit partitioning of nod... |