Barbara Konig. Hypergraph construction and its application to the compositional modelling of concurrency. In GRATRA 2000: Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems, 2000. Proceedings available as Report Nr. 2000-2 (Technische Universitat Berlin).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....components are always adjacent. Furthermore a graph based calculus may serve as a basis for the analysis of mobile processes [4] and as a starting point for a visual concurrent programming language. We also want to demonstrate the usefulness of our graph construction operator (introduced in [5]) which can be used to reason about graphs in an inductive way. When modelling p calculus semantics by graph rewriting, we use hierarchical graphs (our design desicion are explained in more detail in section 4) The encoding of the graph based semantics into the standard semantics requires an ....

.... ) H n ; z n ) or (H 1 ; z 1 ) if n = 1 instead of N n i=1 (H i ; z i ) i i i m H z H h D f i i f Rewriting based on our graph construction operator has the same expressive power as the double pushout approach (with injective production spans) of Ehrig [2] see also [5]) 3 A Name based Notation for Hypergraphs We now introduce a name based notation for hypergraphs which will help us make the transition from the graph rewriting semantics to the standard p calculus. Definition 3 (Name based Graph Terms) Let N be a set of names. A namebased graph term h has one ....

Barbara Konig. Hypergraph construction and its application to the compositional modelling of concurrency. In GRATRA '2000, 2000.

....side R are both hypergraphs of the same arity. Then R is the smallest relation generated by the pairs of R and closed under hypergraph construction. In our approach we generate the same transition system as in the double pushout approach to graph rewriting described in [2] for details see [13]) We need one more concept: a linear mapping which is an inductively de ned transformation, mapping hypergraphs to hypergraphs and adding annotation. De nition 5. Linear Mapping) A function from hypergraphs to hypergraphs is called aritypreserving if it preserves arity and isomorphism classes ....

Barbara Konig. Hypergraph construction and its application to the compositional modelling of concurrency. In GRATRA 2000: Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems, 2000. Proceedings available as Report Nr. 2000-2 (Technische Universitat Berlin).

....side R are both hypergraphs of the same arity. Then R is the smallest relation generated by the pairs of R and closed under hypergraph construction. In our approach we generate the same transition system as in the doublepushout approach to graph rewriting described in [2] for details see [13]) We need one more concept: a linear mapping which is an inductively de ned transformation, mapping hypergraphs to hypergraphs and adding annotation. De nition 5. Linear Mapping) A function from hypergraphs to hypergraphs is called arity preserving if it preserves arity and isomorphism classes ....

Barbara Konig. Hypergraph construction and its application to the compositional modelling of concurrency. In GRATRA 2000: Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems, 2000.

....work on generic type systems for process graphs [10] and to extend it to more general graph rewrite systems. Furthermore we plan to investigate the connection between our approach to model Petri nets and existing approaches as in [13, 12] Remark: this technical report is the extended version of [11]. Acknowledgements: I would like to thank my colleagues and my former advisor J urgen Eickel. Furthermore I want to express my gratitude to the anonymous referees for their valuable comments. ....

Barbara Konig. Hypergraph construction and its application to the compositional modelling of concurrency. In GRATRA '2000: Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems, 2000. to appear.

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Barbara Konig. Hypergraph construction and its application to the compositional modelling of concurrency (full version). Technical Report TUM-I0003, Technische Universitat Munchen, 2000.

....components are always adjacent. Furthermore a graph based calculus may serve as a basis for the analysis of mobile processes [K on99] and as a starting point for a visual concurrent programming language. We also want to demonstrate the usefulness of our graph construction operator (introduced in [K on00b]) which can be used to reason about graphs in an inductive way. When modelling calculus semantics by graph rewriting, we adhere to the following principle: we utilize well known hypergraphs [Hab92] and a replacement mechanism equivalent to the doublepushout approach [Ehr79] We only use standard ....

....and thereby determine the string of external nodes of the result. Rewriting based on our graph construction operator has the same expressive power as the graph expressions by Bauderon and Courcelle [BC87] or the double pushout approach (with injective production spans) of Ehrig [Ehr79] see also [K on00b]) 1 [n] stands for the set f1; ng. 2 3 A Name based Notation for Hypergraphs We now introduce a name based notation for hypergraphs which will help us make the transition from the graph rewriting semantics to the standard calculus. De nition 3 (Name based Graph Terms) Let N be a ....

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Barbara Konig. Hypergraph construction and its application to the compositional modelling of concurrency. In GRATRA '2000: Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems, 2000. Proceedings available as Report Nr. 2000-2 (Technische Universitat Berlin).

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