J. Engelfriet. A multiset semantics for the pi-calculus with replication. Theoret. Cornput. Sci., 153:65-94, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....that has to be ignored to preserve the semantics of processes. The late introduction of the replication operator may explain why, to the best of our knowledge, investigations on its causal semantics are scarce in the literature. We are only aware of the work by Engelfriet (see e.g. [9]) where a Petri nets semantics for the r calculus with replication is proposed, using possibly infinite markings. Such a state of affairs is unfortunate, since causality is often advocated to sharpen the description of distributed systems, because it may lead to more accurate guidelines to ....

J. Engelfriet. A multiset semantics for the pi-calculus with replication. Theoret. Cornput. Sci., 153:65-94, 1996.

....process terms of the calculus are considered, and proven to be decidable and to have axiomatizations that are sound and complete in the multiset semantics M of the calculus. All three are strong simulation relations. Introduction This paper is a sequel to [2] which, in turn, is a sequel to [1]. The reader is therefore assumed to be familiar with the concepts and results of [1] and, more in particular, those of [2] In [2] it was proven that in the calculus with replication, two processes are structurally congruent (for a natural extension of the structural congruence of [6] if and ....

....have axiomatizations that are sound and complete in the multiset semantics M of the calculus. All three are strong simulation relations. Introduction This paper is a sequel to [2] which, in turn, is a sequel to [1] The reader is therefore assumed to be familiar with the concepts and results of [1], and, more in particular, those of [2] In [2] it was proven that in the calculus with replication, two processes are structurally congruent (for a natural extension of the structural congruence of [6] if and only if they correspond to the same solution, i.e. the same multiset of the multiset ....

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J. Engelfriet, A multiset semantics for the pi-calculus with replication, The36 oret. Comput. Sci. 153 (1996) 65-94.

....j x 2 Xg, and similarly for more complicated data structures. Rather than defining a general notion of data structure, our axioms just formulate some obvious laws that these mappings should satisfy. Our interest in graphs of a type more general than the usual ones came from our investigation [2, 3, 4] into the structure of object oriented parallel systems, in particular the processes of the calculus (see [14, 13] In general, a (massively) parallel system can be viewed as a (large) collection of (active) objects that communicate with each other through the use of common resources. The ....

....consider hypergraphs (where each object is just a set of resources) because we do not wish to abstract from the internal structure of an object, such as the order in which it uses its resources and the actions it executes inbetween. As a concrete example, a process of the calculus is modeled in [2] as a (multi )set of objects, where each object is an (unordered, possibly infinite) tree of which the nodes are labeled by channel names. Such an object communicates with other objects through channels, which are the resources; the tree indicates the partial order between the communications that ....

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J. Engelfriet, A multiset semantics for the pi-calculus with replication, Theoret. Comput. Sci. 153 (1996) 65--94.

....6 we state the main results. Section 7 contains the proofs of results (A) B) A 0 ) and the only if part of (B 0 ) The if part of result (B 0 ) and result (C 0 ) are proved in the sequel paper [9] A previous version of this paper was published in the Proceedings of CONCUR 93 [8]. 2 The Small Calculus We briefly recall the definition of the small calculus from [13] Let N be an infinite set of names. The context free syntax for process terms is as follows (where we use a comma rather than j to separate alternatives) P : xy:P ; x(y) P ; 0 ; P j P ; P ; y)P with ....

J.Engelfriet; A multiset semantics of the pi-calculus with replication, in Proc.CONCUR'93, Lecture Notes in Computer Science 715, Springer-Verlag, 1993, 7-21

....by the structures of a special structure system called the multi structure system of S. Thus, the proof is by an application of the results in the previous section. In a Petri net (or multiset transition system) a multiset is exactly the mathematical concept that fits the notion of concurrency. In [4, 5] for instance, the semantics of a calculus term is a multiset of structured objects composed of names. In other fields of computer science multisets are used to model databases for example. In [7] an algebra for nested multisets is presented to model hierarchical data structures. As usual, a ....

....i.e. directed graphs with multiple edges: a pair of nodes can be joined by more than one edge. Isomorphism of such multi S structures is the usual isomorphism of multi graphs. 3) Solutions in the Multiset Calculus. A typical example of multisets of structured objects can be found in [4, 5]. For S = Mol; New; ff; multi S structures are called solutions, where New is the set of new names, building molecules as structured objects which in turn form the set Mol. The semantics of a process term of the calculus of [11] is defined to be such a solution, modulo an injective ....

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J. Engelfriet, A multiset semantics for the pi-calculus with replication, Theoret. Comput. Sci. 153 (1996) 65-94.

....respect to the static operations) that satisfies the given structural laws. Also, process terms with the same flowgraph have the same behaviour, where, in this case, same means strongly bisimilar . The corresponding laws for strong bisimilarity are the static laws in Section 3. 4 of [6] In [2, 3] a multiset semantics (or Petri net semantics) of the calculus of [7] is given that is closely related to the structural approach. A transition system M is defined of which the states are solutions , which are multisets of molecules, and a molecule is a guarded solution (the chemical ....

....where several copies of the same molecule may be present in the solution. In accordance with the operation of replication, there may even be infinitely many such copies. Moreover, a semantic mapping is defined that associates with each process term of the calculus a state of M . It is proved in [2, 3] that the semantic mapping is a strong bisimulation between a process term and its corresponding multiset in M . Thus, from the interleaving point of view they have the same behaviour. The gain is that, intuitively, the behaviour of the multiset in M is the true concurrency behaviour of the ....

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J.Engelfriet; A multiset semantics of the pi-calculus with replication, Report 94-26, Department of Computer Science, Leiden University, August 1994

....respect to the static operations) that satisfies the given structural laws. Also, process terms with the same flowgraph have the same behaviour, where, in this case, same means strongly bisimilar . The corresponding laws for strong bisimilarity are the static laws in Section 3. 4 of [6] In [2, 3] a multiset semantics (or Petri net semantics) of the calculus of [7] is given that is closely related to the structural approach. A transition system M is defined of which the states are solutions , which are multisets of molecules, and a molecule is a guarded solution (the chemical ....

....where several copies of the same molecule may be present in the solution. In accordance with the operation of replication, there may even be infinitely many such copies. Moreover, a semantic mapping is defined that associates with each process term of the calculus a state of M . It is proved in [2, 3] that the semantic mapping is a strong bisimulation between a process term and its corresponding multiset in M . Thus, from the interleaving point of view they have the same behaviour. The gain is that, intuitively, the behaviour of the multiset in M is the true concurrency behaviour of the ....

[Article contains additional citation context not shown here]

J.Engelfriet; A multiset semantics of the pi-calculus with replication, in Proc.CONCUR'93, Lecture Notes in Computer Science 715, Springer-Verlag, 1993, 7-21

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