H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....chapter the main de nitions and results of high level replacement systems are introduced. Moreover, several results are shown that are especially important for the abstract component framework introduced in chap. 2. HLR systems as an abstraction of graph transformation systems were introduced in [6]. The main idea was to have a framework that re ects the shared properties of di erent transformation based speci cation approaches. Several instantiations have been examined by now, for example: graph transformations, algebraic speci cations and di erent kinds of petri nets. A detailed ....

....e; b 2 ; d are assumed to be injective. Now we have that (1) is a pushout. 2) b1 Remark: These theorems correspond to the assumptions 8, 7, 9 and 10. Their validity follows from the the fact that the category P=T is based on sets and the corresponding properties hold in SET. See [6] for detailed proofs. Now we have the following results. A petri net component now consists of three place transition nets: a net IMP , called import interface, a net EXP , called export interface and a net BOD, called body. Moreover, the component contains an injective petri net ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. volume 1 of Math. Struct. in Comp. Science, pages 361-404. Cambridge Univ. Press, 1991.

....important difference. We often employ similar constructions (like completion of a net to a cycle, see e.g. vdA97] which are applied to the class of marked place transition nets. Moreover, we use a formal notion of rules for which e.g. compatibility concerning structuring is already available [EHKP91]. The paper is organized as follows: In Section II our approach is illustrated by the development of a small producer consumer system. In Section III we state our first main theorem (Theorem 18: Collapsing Morphisms Respect Liveness) after introducing the corresponding notion of morphism. In ....

....Theorem 18 (Coll. Morphisms Respect Liveness) Given a collapsing morphism f : N 1 N 2 and let N 2 be live, then N 1 is live as well. The proof see [GPU01] 2 IV. REVIEW AND EXTENSION OF THE Q THEORY In this section we mainly review the notions introduced for high level replacement systems [EHKP91] and their extension to Q morphisms [Pad99] We extend the theory for Q transformations slightly in order to include certain compatibility restrictions. A. Basic Ideas of High Level Replacement Systems Here we just give the basic definitions. The underlying assumptions and conditions can be ....

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361--404, 1991.

....with re nement. In this paper we consider our notion of rule based modi cation of algebraic high level nets (developed in [30] and extend it to rule based re nement preserving safety properties. The theory of rule based modi cation is an instance of the theory of high level replacement systems [9], a generalization of graph transformation [10] in a categorical way. Rules describe which parts of a net are to be deleted (left side of the rule) and which new parts are to be added (right side of the rule) This transformation of nets yields a resulting net which is well de ned and no unspeci ....

H. Ehrig, A. Habel, H.-J. Kreowski and F. Parisi-Presicce. Parallelism and Concurrency in High-Level Replacement Systems. In Math. Struct. in Comp. Science, Vol. 1 (1991), 361-404.

....in a rule based manner where a rule shows part of a model in a before after style. This allows a clear, consistent and intuitive description of evolution steps. We generalize the graph transformation concepts to other specification techniques, yielding distributed high level replacement systems [EHKP91] ffl Allowing a variety of visual modeling techniques for both the architectural and the specification level of model evolution, we need a Generic Visual Modeling Approach to deal with the representation of arbitrary visual models and their dynamic behavior. The GENGED approach is based on ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361--404, 1991.

....rules and transformations that preserve safety properties. On the other hand we use rules that introduce new safety properties. The notion of rules for Petri nets is based on transformations within the abstract frame of high level replacement (HLR) systems. HLR systems have been introduced in [EHKP91] as a categorical generalization of the double pushout approach to graph transformations. The application of high level replacement systems to a special domain as place transition nets, algebraic specification etc. requires a suitable category, a class of distinguished morphisms, and the ....

....this significantly decreases the cost of proving safety properties. do m f o dc c f r rq nrq do m f o dc c f Figure 6: Rule r rq fin 3 Review of High Level Replacement Systems In this section we briefly review the concepts of high level replacement (HLR) systems in the sense of [EHKP91], a categorical generalization of graph grammars. These concepts are mainly needed for our proofs in Section 4 and may be skipped by readers familiar with the theory of HLR and Q transformations. High level replacement systems are formulated for an arbitrary category C with a distinguished class ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce, Parallelism and concurrency in high-level replacement systems, Math. Struct. in Comp. Science 1 (1991), pp. 361--404.

....complete the scheme. Algebraic High Level Nets (AHL nets) consist roughly speaking of a Petri net with inscriptions of an algebraic specication SPEC [EM85] dening the data type part of the net. For AHL nets structuring techniques are formulated within the frame of high level replacement systems [EHKP91b]. Results from the theory of AHL nets [PER95, PGE98, GE99] comprise horizontal structuring techniques like union (composition of two nets with respect to a common interface) and fusion (the gluing of subnets within a given net) and vertical structuring like rule based modication and rule based ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361404, 1991.

....the doors using rules and transformations that preserve safety properties. Thus we gain a model of the elevator with request, that satisfies the safety properties concerning the doors without proving these properties again for this new model. High level replacement systems have been introduced in [EHKP91] as a categorical generalization of the double pushout approach to graph transformations, there the first application to place transition nets has been given as well. The application of high level replacement systems to a special domain as place transition nets, algebraic specification etc. ....

....3 leads to the place transition net E 2 . E 2 is a more detailed model of the elevator system or in other words a refinement of the original model E 0 . 3 Review of High Level Replacement Systems In this section we review most shortly the concepts of high level replacement systems in the sense of [EHKP91], a categorical generalization of graph grammars. High level replacement systems are formulated for an arbitrary category C with a distinguished class M of morphisms which is used to classify different types of rules. Thus, high level replacement systems allow a great variety of interpretations of ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi Presicce, Parallelism and concurrency in high-level replacement systems, Math. Struct. in Comp. Science 1 (1991), 361--404.

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361-404, 1991.

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high level replacement systems. Technical Report 90-35, Technical University of Berlin, 1990.

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361-404, 1991.

....6 leading to high level abstract Petri nets in Section 7. In Section 8 we study rulebased re nement and horizontal structuring. Rule based re nement is studied within the frame of high level replacement systems. Results concerning independence, and parallelism of derivations, as given in [EHKP91b] are extended to a new type of rules, which allow us to consider di erent kinds of re nement as special cases [Pad99b] Horizontal structuring is given by the notions of union and fusion, motivated by the constructions in [Jen92] but they are de ned in a categorical way independently of Petri ....

....results make use of this close relation between the categorical concepts of rule based re nement and horizontal structuring. In fact, all of them are based on speci c colimits. Since the general theory of rule based re nement is presented in the frame of high level replacement systems (see [EHKP91b,Pad99b] the proofs in Appendix B make use of speci c conditions for high level replacement systems. The underlying theory of high level replacements is given purely categorical, so we formulate the following notions and results in these terms. The application to abstract Petri nets is due to ....

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361-404, 1991.

....called re nement morphism, which allows to map transformations and processes in EXP to composite transformations and processes in BOD. More generally, we could require that a re nement morphism exp : EXP BOD is a transformation from EXP to BOD in the sense of high level replacement systems [EHKP91]. This would mean that exp : EXP = BOD is a transformation sequence induced by some high level rules r : L R where L and R are integrated speci cations in the sense of section 2. It remains open to de ne syntax and semantics of re nement morphisms and corresponding variants of our ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in High Level Replacement Systems. Math. Struc. in Comp. Science, 1:361-404, 1991.

....system, where the distinguished class M is given by strict morphisms. Fact 3.4 (PT is High Level Replacement System) The category PT as de ned in Def. 3.2 together with strict morphisms forms a high level replacement system. i.e. the HLR conditions of Def. A.5 are satis ed. Proof For a proof see [EHKP91b, Pad93]. p 3.2 Category EN of Elementary Nets De nition 3.5 (Elementary Net) An elementary net is given by N = P; T ; pre; post) with P the set of places, T the set of transitions, pre; post : T P(P ) the pre and postdomain of transitions. 2 De nition 3.6 (Elementary Net Morphisms) Given N i = P i ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361-404, 1991.

....marked place transition nets. We therefore employ similar constructions (like completion of a net to a cycle) which become more complex in the case of marked place transition nets. Moreover, we use a formal notion of rules for which e.g. compatibility concerning structuring are already available [EHKP91,EGP99]. In our approach, the notion of morphism is essential. We employ morphisms which are more or less special cases of vicinity respecting morphisms, see [DM90] They allow the abstraction of a (transition bordered) subnet to a single transition, but not dually for places like in [DM90] We lifted ....

....of all transitions in a collapsed subnet. Here, the construction has been demonstrated informally on a simple example. The formal description is in the proof of Theorem 1. 4 Review and Extension of Q In this section we mainly review the notions introduced for high level replacement systems [EHKP91] and their extension to Q morphisms [Pad99a] We extend the theory forQ transformations slightly in order to include certain compatibility restictions. 4.1 Basic Ideas of High Level Replacement Systems Here we just give the basic de nitions. The underlying assumptions and conditions are given in ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361-404, 1991.

No context found.

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361-404, 1991.

....can be considered as a general description of replacement systems, where a left hand side is replaced by a right hand side. Rules and transformations capture this replacement and thus define any kind of system development or modification. High level replacement systems have been introduced in [EHKP91b] as a categorical generalization of graph transformations. The application of high level replacement systems to different domains as place transition nets, algebraic specification [EGP99] etc. requires a suitable category and the satisfaction of the HLR conditions. High level replacement systems ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Computer Science, 1:361--404, 1991.

....integrated with behavioural constraints. A final coalgebraic semantics for graph transformation systems with constraints in general has been developed and specialised to temporal logic constraints. It shall be stressed that these notions and results can be generalised to arbitrary HLR categories [14] in order to transfer them to the transformation other kinds of objects like hypergraphs, attributed graphs, and relational structures. Behavioural constraints, as an abstract framework, are comparable to control conditions in GRACE, a graph and rule based specification language that is being ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce, "Parallelism and concurrency in High Level Replacement Systems," Math. Struc. in Comp. Science, vol. 1, pp. 361--404, 1991.

....via such rules. Applying this result to LISP it is shown that a LISP interpreter presented by a graph grammar is correct with respect to the functional semantics of graph like LISP expressions. High Level Replacement Systems The high level replacement (HLR) systems, introduced in [EHKP91a, EHKP91b] abstract from concrete categories of graphs to more general categories in such a way that the well known and desired properties concerning parallelism and concurrency are guaranteed. This yields a categorical framework for different types of replacement systems for complex objects, including ....

....global states. This result holds for strict interface preserving derivations while in general distributed derivations are not reducible to global state derivations. Classical results concering parallelisms and concurrency have been generalized to high level replacement systems [EHKP91a, EHKP91b, ET92] They are formulated in an axiomatic framework based on categories and double pushouts. The basic notions, like productions, parallel and sequential independence, are introduced for those systems and lead to Church Rosser, Parallelism and Concurrency Theorems. Specific conditions, called ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361--404, 1991.

....signatures and constraints as sentences. Then lemma 3.7 turns out to be the satisfaction condition and is sufficient to prove the local confluence and the Parallelism Theorem. Because of their categorical nature, application conditions can easily be adopted to high level replacement systems (see [10], 11] as well as to graph structures (see [18] Doing so they become available to a big variety of transformation systems. ....

Hartmut Ehrig, Annegret Habel, Hans-Jorg Kreowski, Francesco Parisi-Presicce. Parallelism and concurrency in high level replacement systems. Mathematical Structures in Computer Science 1, 361--404, 1991.

..... p 1 ) p 2 ) p 1 ) p 2 Figure 25: Two s derivations Figure 26: Two s concurrent rules A connection between sequentially s dependent direct derivations and s concurrent derivations is expressed by the following result. Up to now, the result was only known for DPO i=a (see [EHR86, EHKP91] Theorem 8.8 (Concurrency I) In DPO i=a and DPO a=a the following holds: 1) For every pair of sequentially s dependent direct derivations G ) p 1 H ) p 2 M there is an s concurrent derivation G ) Con(p 1 ;s;p 2 ) M . 2) For every s concurrent derivation G ) Con(p 1 ;s;p 2 ) M there are ....

....information on the given direct derivations as our definition of strong sequential independence. A further topic is to consider so called high level replacement systems, that is, double pushout derivations in arbitrary categories. We just mention that our results do not follow from the ones in [EHKP91] where non injective rules and injective matching morphisms are not considered. Finally, the computability model for graph functions introduced in Subsection 4.2 should be further investigated. Since this model does not cover all computable (in the ordinary sense) functions on graphs, there is ....

[Article contains additional citation context not shown here]

Hartmut Ehrig, Annegret Habel, Hans-Jorg Kreowski, Francesco Parisi-Presicce. Parallelism and concurrency in high level replacement systems. Mathematical Structures in Computer Science 1, 361--404, 1991.

....over a dependency relation D between the right hand side object of the first production and the left hand side object of the second production. The resulting composite production is called D concurrent production. We recall the notion for double pushout high level replacement systems as given in [4]. To guarantee that all necessary constructions exist, we assume so called HLR2 categories, which are defined in the Appendix (according to [6] Definition 13 (Concurrent DPO production) 1. Let p = L K # R) and p # = L # K # # R # ) be two productions and let D be an object together ....

....for redundant productions, namely by finding a match of L # in R. L # fflffl (PO) K # fflffl oo (PO) R # fflffl L K R (PB) K ## oo R ## K ### aaC C C C C C C C y y y y y y y y Using the following fact, which is proved for double pushout high level replacement systems in [4] as analysis step of the so called Concurrency Theorem, we can show that a production q is redundant if it is subsumed by a composite production. Fact 14. Given a direct derivation G # H via a composite production p # q there is a derivation sequence G # X # H via (p, q) ## Theorem ....

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Mathematical Structures in Computer Science, 1:361--404, 1991.

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1, 1991.

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Mathematical Structures in Computer Science, 1(3):361--404, November 1991.

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H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1, 1991.

No context found.

H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361--404, 1991.

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