## Graph Rewriting, Constraint Solving and Tiles for Coordinating Distributed Systems (1999)

Venue: | Applied Categorical Structures |

Citations: | 17 - 14 self |

### BibTeX

@ARTICLE{Montanari99graphrewriting,,

author = {Ugo Montanari and Francesca Rossi},

title = {Graph Rewriting, Constraint Solving and Tiles for Coordinating Distributed Systems},

journal = {Applied Categorical Structures},

year = {1999},

volume = {7},

pages = {7--333}

}

### OpenURL

### Abstract

. In this paper we describe an approach to model the dynamics of distributed systems. For distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. The basic idea is to use graphs to represent states of such systems, and graph rewriting to represent their evolution. The kind of graph rewriting we use is based on simple context-free productions which are however combined by means of a synchronization mechanism. This allows for a good level of expressivity in the system without sacrifying full distribution. To formally model this kind of graph rewriting, however, we do not adopt the classical graph rewriting style but a more general framework, called the tile model, which allows for a clear separation between sequential rewriting and synchronization. Then, since the problem of satisfying the synchronization requirements may be a complex combinatorial pro...

### Citations

1286 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ...of possible rewritings, are modeled by a simple version of tile transition systems where sequents have the form s ! t. Rewriting models from which the tile model drew inspiration are the sos approach =-=[38]-=- and the rewriting logic approach [32]. But the work which is most related to the tile model is that on context systems [27]. However, the tile model allows for more general formats, where e.g. each p... |

1000 |
Consistency in networks of relations
- Mackworth
- 1977
(Show Context)
Citation Context ... in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [30, 35], and the propagation and solution techniques associated to them =-=[30, 35, 29, 19, 31, 12]-=-, may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset... |

565 | Term Rewriting Systems
- Klop
- 1992
(Show Context)
Citation Context ...ne both by requiring certain synchronizations among sub-parts of the system and by defining the effects of a rewriting (to be used by subsequent rewritings). Thus, for example, term rewriting systems =-=[26]-=-, which do not allow for any synchronization nor restriction on the class of possible rewritings, are modeled by a simple version of tile transition systems where sequents have the form s ! t. Rewriti... |

473 |
Conditional rewriting logic as a unified model of concurrency
- Meseguer
- 1992
(Show Context)
Citation Context ... a simple version of tile transition systems where sequents have the form s ! t. Rewriting models from which the tile model drew inspiration are the sos approach [38] and the rewriting logic approach =-=[32]-=-. But the work which is most related to the tile model is that on context systems [27]. However, the tile model allows for more general formats, where e.g. each process variable can appear several tim... |

423 |
Networks of constraints: fundamental properties and application to picture processing
- Montanari
- 1974
(Show Context)
Citation Context ...ng context-sensitive rule. Of course, all these tasks are to be performed in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems =-=[30, 35]-=-, and the propagation and solution techniques associated to them [30, 35, 29, 19, 31, 12], may be helpful. A finite domain constraint problem can be described as a set of variables taking values over ... |

389 |
Network-based heuristics for constraint-satisfaction problems
- Dechter, Pearl
- 1987
(Show Context)
Citation Context ... in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [30, 35], and the propagation and solution techniques associated to them =-=[30, 35, 29, 19, 31, 12]-=-, may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset... |

264 |
The complexity of some polynomial network consistency algorithms for constraint satisfaction problems
- Mackworth, Freuder
- 1985
(Show Context)
Citation Context ... in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [30, 35], and the propagation and solution techniques associated to them =-=[30, 35, 29, 19, 31, 12]-=-, may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset... |

249 | Distributed Constraint Satisfaction: foundations of cooperation in multi-agent systems
- Yokoo
- 2001
(Show Context)
Citation Context ...acktracking search algorithm (as described above), which however has to be distributed as well. Examples of distributed version of such algorithm for finite domain constraint problems can be found in =-=[42, 43]-=-. In the following of this paper, we provide the details on the formalisms and the techniques we informally described in the introduction, and on the way they can be used for our purposes. In particul... |

245 |
Synthesizing Constraint Expressions
- Freuder
- 1978
(Show Context)
Citation Context |

185 |
Initial Algebra Semantics and Continuous Algebras
- Goguen, Thatcher, et al.
- 1977
(Show Context)
Citation Context ... g(b)), respectively, for a given variable x. In fact, a classical result we already anticipated proves that algebraic theories are equivalent to the ordinary construction (as it can be found e.g. in =-=[16]-=-) for term algebras. Proposition 2. (algebraic theories and term algebras) Let \Sigma be a signature. Then for all n; m 2 IlN there exists a one-to-one correspondence between the set of arrows from n ... |

173 |
Introduction to the algebraic theory of graph grammars (a survey). in proc. of int'l workshop on Graph-Grammars and their Application to Com
- Ehrig
- 1979
(Show Context)
Citation Context ...ore complex distributed systems. 1. Introduction Among the many formalisms that can be chosen to represent distributed systems and their evolutions, we believe that graphs and graph rewriting systems =-=[14, 15, 39, 40, 9]-=- are one of the most convenient, both in terms of expressivity and of technical background. In fact, graphs describe in a natural way net topologies and data sharing, and moreover they possess a wide ... |

166 | Functorial Semantics of Algebraic Theories - Lawvere - 1963 |

109 | From local to global consistency
- Dechter
- 1992
(Show Context)
Citation Context ...ntation, to achieve a great amount of redundancy removal, and thus a great improvement in the solution process, in many cases, which are related for example to the structure of the constraint problem =-=[10]-=-, or to the semantics of the constraints [35], or to the size of the domains [10], or also to the tightness of the constraints [41]; \Gamma distributed backtracking has been shown to be convenient whe... |

82 | Rewriting Logic as a Semantic Framework of Concurrency: a Progress Report
- Meseguer
- 1996
(Show Context)
Citation Context ...etri nets equipped with flexible synchronization primitives and inspired by the tile model are presented in [3, 4]. Finally, it is studied in [34] how to translate the tile model into rewriting logic =-=[33]-=-, in order to take advantage of important features of the latter, like execution strategies and reflective logics, and to employ its existing implementations. While modeling our notion of graph rewrit... |

73 |
Compositionality through an operational semantics of contexts
- Larsen, Liu
- 1991
(Show Context)
Citation Context ...ting models from which the tile model drew inspiration are the sos approach [38] and the rewriting logic approach [32]. But the work which is most related to the tile model is that on context systems =-=[27]-=-. However, the tile model allows for more general formats, where e.g. each process variable can appear several times in process contexts (see [23], Definition 22). The name of the tile model comes fro... |

65 | The tile model
- Gadducci, Montanari
- 2000
(Show Context)
Citation Context ...se instead a simpler graph rewriting approach, since we are just interested in the present of the system, and not in its history. Moreover, we model this kind of graph rewriting within the tile models=-=[23]-=-, a general framework which allows for a clear and formal separation between sequential evolution and synchronization. This is in line with most coordination languages and models [5], which separate t... |

50 | Hyperedge Replacement: Grammars and Languages - Habel - 1992 |

44 |
A model of distributed systems based on graph rewriting
- Degano, Montanari
- 1987
(Show Context)
Citation Context ...ay move without any need of communicating with each other: each process needs only know its context-free productions. This kind of synchronization and process evolution has been already considered in =-=[11]-=-, and modeled via a special graph rewriting formalism, called grammars for distributed systems (GDS), where graphs represented not only the current state of the system but also its history, so to be a... |

43 | Analysis of distributed arc-consistency algorithms
- Baudot, Deville
- 1997
(Show Context)
Citation Context ... which represent the selected subproblems. In particular, the arc-consistency algorithm can be implemented in a completely distributed environment, since each agent corresponds to just one constraint =-=[37]-=-. Once a local consistency algorithm has been applied over the current state of the system, so to possibly eliminate some redundant choices for the processes, one has however still the problem of solv... |

38 | An Algebraic Presentation of Term Graphs, via GSMonoidal Categories. Applied Categorical Structures 7:299–331
- Corradini, Gadducci
- 1999
(Show Context)
Citation Context ... is interesting to remark that this construction can be characterized as universal. Tiles have already been used to model several formalisms. For example, the combined used of tiles and term graphs 1 =-=[1, 7, 8] for-=- modeling asynchronous ��-calculus and CCS with locations has been described in [16, 17, 18]. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the t... |

35 |
Backtrack-Free and BacktrackBounded Search
- Freuder
- 1988
(Show Context)
Citation Context ...he productions of adjacent processes). This could lead to a great speed-up in the overall search for a solution, especially when the graph representing the current system state has special topologies =-=[20]-=-. In classical constraint solving over finite domains, constraints are usually stored in one memory. Thus local consistency algorithms are usually centralized. However, it is easy to see that such alg... |

34 | A 2-categorical presentation of term graph rewriting
- Corradini, Gadducci
- 1997
(Show Context)
Citation Context ... is interesting to remark that this construction can be characterized as universal. Tiles have already been used to model several formalisms. For example, the combined used of tiles and term graphs 1 =-=[1, 7, 8] for-=- modeling asynchronous ��-calculus and CCS with locations has been described in [16, 17, 18]. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the t... |

30 |
Review of the elements of
- Kelly, Street
- 1974
(Show Context)
Citation Context ...her, while sequential composition corresponds to vertical justapposition of tiles and synchronization to horizontal justapposition. The tile model can also be characterized by using double-categories =-=[25, 23]-=-, which can be seen as the superposition of a vertical and an horizontal category. Starting from a tile transition system, it is in fact possible to obtain a double-category whose cells directly corre... |

24 | On the Algebraic Approach to Concurrent Term Rewriting
- Gadducci
- 1996
(Show Context)
Citation Context ... theory similar to, but weaker then, the ordinary algebraic theory of terms and substitutions. In the Appendix we give the finitary axiomatization of (one sorted) gs-monoidal theories as presented in =-=[21, 23, 7, 8]-=-. The models of gs-monoidal theories are gs-monoidal categories, a special case of symmetric monoidal categories. Here we present an algebra of open graphs which coincides with the algebra in the Appe... |

20 | Equational reasoning with 2-dimensional diagrams - Lafont - 1995 |

19 | F.: Graph rewriting and constraint solving for modelling distributed systems with synchronization (extended abstract - Montanari, Rossi - 1996 |

17 | Zero-Safe Nets, or Transition Synchronization Made Simple
- Bruni, Montanari
- 1997
(Show Context)
Citation Context ...��-calculus and CCS with locations has been described in [16, 17, 18]. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the tile model are presented=-= in [3, 4]-=-. Finally, it is studied in [34] how to translate the tile model into rewriting logic [33], in order to take advantage of important features of the latter, like execution strategies and reflective log... |

17 | Constraint tightness versus global consistency
- Beek, Dechter
- 1994
(Show Context)
Citation Context ...h are related for example to the structure of the constraint problem [10], or to the semantics of the constraints [35], or to the size of the domains [10], or also to the tightness of the constraints =-=[41]-=-; \Gamma distributed backtracking has been shown to be convenient when the structure of the process connection is not too dense [42]; thus in this cases the performance of this way of solving the rule... |

14 |
Tiles for Concurrent and Located Calculi
- Ferrari, Montanari
- 1997
(Show Context)
Citation Context ...e already been used to model several formalisms. For example, the combined used of tiles and term graphs 1 [1, 7, 8] for modeling asynchronous ��-calculus and CCS with locations has been described=-= in [16, 17, 18]-=-. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the tile model are presented in [3, 4]. Finally, it is studied in [34] how to translate the tile mode... |

14 | Rewriting rules and CCS
- Gadducci, Montanari
- 1996
(Show Context)
Citation Context ... in sequential agents and coordinators not only statically but also dynamically. Thus the separation concerns not only the structure of the system but also its behavior. More formally, the tile model =-=[23, 22]-=- describes the behavior of a wide class of systems via certain rewriting rules. These rules define a transition system where both the states and the transitions may be complex and be equipped with an ... |

13 | Zero-Safe Nets: The Individual Token Approach
- Bruni, Montanari
- 1998
(Show Context)
Citation Context ...��-calculus and CCS with locations has been described in [16, 17, 18]. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the tile model are presented=-= in [3, 4]-=-. Finally, it is studied in [34] how to translate the tile model into rewriting logic [33], in order to take advantage of important features of the latter, like execution strategies and reflective log... |

10 | Encyclopedia of AI, chapter Constraint Satisfaction - Mackworth - 1988 |

8 | Semantics of weakening and contraction. Annals of pure and applied logic - Jacobs - 1994 |

7 |
Specifying highly concurrent data structure manipulation
- CORRADINI, DEGANO, et al.
- 1985
(Show Context)
Citation Context ...rrency and dependency information among the various computation steps. Also, a variation of GDSs which uses a more general rewriting mechanism allowing for system reconfiguration has been proposed in =-=[6]-=-. In this paper we use instead a simpler graph rewriting approach, since we are just interested in the present of the system, and not in its history. Moreover, we model this kind of graph rewriting wi... |

5 |
Asynchronous weak-committment search for solving distributed constraint satisfaction problems
- Yokoo
- 1995
(Show Context)
Citation Context ...acktracking search algorithm (as described above), which however has to be distributed as well. Examples of distributed version of such algorithm for finite domain constraint problems can be found in =-=[42, 43]-=-. In the following of this paper, we provide the details on the formalisms and the techniques we informally described in the introduction, and on the way they can be used for our purposes. In particul... |

4 | Relating Two Categorical Models of Concurrency - Corradini, Gadducci, et al. - 1995 |

1 |
Harald-Reto Fonio, and Annegret Habel. Amalgamation of graph transformations: A synchronization mechanism
- Boehm
- 1987
(Show Context)
Citation Context ...ormalisms, which range from the simplest context-free edge rewriting [24], to the more general context-sensitive subgraph rewriting [14, 15], to synchronized rewriting via the concept of amalgamation =-=[2]-=-. In order to choose one of them to model the evolution of a distributed system, we must make some assumptions on the system we want to model. For this paper, we assume that processes, in order to evo... |

1 |
A Tile-Based Coordination View of ��-Calculus
- Ferrari, Montanari
- 1997
(Show Context)
Citation Context ...e already been used to model several formalisms. For example, the combined used of tiles and term graphs 1 [1, 7, 8] for modeling asynchronous ��-calculus and CCS with locations has been described=-= in [16, 17, 18]-=-. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the tile model are presented in [3, 4]. Finally, it is studied in [34] how to translate the tile mode... |

1 |
Tile Formats for Located and Mobile Systems, paper submitted for publication
- Ferrari, Montanari
(Show Context)
Citation Context ...e already been used to model several formalisms. For example, the combined used of tiles and term graphs 1 [1, 7, 8] for modeling asynchronous ��-calculus and CCS with locations has been described=-= in [16, 17, 18]-=-. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the tile model are presented in [3, 4]. Finally, it is studied in [34] how to translate the tile mode... |

1 |
Mapping Tile Logic into Rewriting Logic, in: Francesco Parisi-Presicce
- Meseguer, Montanari
- 1998
(Show Context)
Citation Context ... has been described in [16, 17, 18]. Also, extensions of Petri nets equipped with flexible synchronization primitives and inspired by the tile model are presented in [3, 4]. Finally, it is studied in =-=[34]-=- how to translate the tile model into rewriting logic [33], in order to take advantage of important features of the latter, like execution strategies and reflective logics, and to employ its existing ... |