D. M. R. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, In Proc. of the 5th GI Conference, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer Verlag, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Moreover, it is argued that the undecidability of hhp bisimilarity holds for nite elementary net systems and 1 safe Petri nets. 1. INTRODUCTION The notion of behavioural equivalence which has attracted most attention in concurrency theory is bisimilarity, originally introduced by Park [25] and Milner [19] concurrent programs are considered to have the same meaning if they are bisimilar. The prominent role of bisimilarity is due to many pleasant properties it enjoys; we mention a few of them here. A process of checking whether two transition systems are bisimilar can be seen as a ....

D. M. R. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Theoretical Computer Science: 5th GI-Conference, volume 104 of LNCS, pages 167-183. SpringerVerlag, 1981.

....the problem of checking programs with large (possibly in nite) state spaces to checking a transformed property on a suitable small, nite state abstraction of the original program. Typically, the two programs are related by a structural relationship, such as simulation [Mil71] or bisimulation [Par81] This guarantees that if the transformed property holds on the abstract program, then the original property holds on the concrete program. Common examples of abstraction are those resulting from symmetry reduction [ES93,CFJ93] data independence [Wol86] and predicate abstraction [GS97] ....

....properties. 3 Lifting Proofs Given a LTS N that abstracts an LTS M , we show how a proof of a property f on N can be lifted to a proof of the same property on M . We consider two common notions of abstraction: simulation [Mil71] which preserves only universal properties, and bisimulation [Par81] which preserves properties of the full mu calculus (cf. BCG88,Sti95] Let M and N be LTS s, with M = N and M = N . A relation SM SN is a simulation from M to N if, and only if: The initial states of M and N are related, i.e. s M s N , and For every s in SM and t in SN such ....

D. Park. Concurrency and automata on in nite sequences, volume 154 of LNCS. Springer Verlag, 1981.

....cation, etc. In Modal Logic this notion was introduced by van Benthem [Ben76] as an equivalence principle between Kripke structures. In Concurrency Theory it was introduced by Milner and Park for testing observational equivalence of the Calculus of Communicating Systems (CCS) In particular in [Par81] a previous notion of automata simulation by Milner is re ned in the context of omega regular languages for concurrency, while in [Mil90] weak and strong) bisimulation is proposed. In Set Theory, it was introduced by Forti and Honsell [FH83] as a natural principle replacing extensionality in ....

D. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Proc. of 5th Int. Conference on Theoretical Computer Science, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer-Verlag, Berlin, 1981.

....[25] Supported by NSF grant CCR 89 15206, and CCR 92 25124, by ARPA contracts N00014 89 J 1988 and N00014 92 J 4033, and by ONR contract N00014 91 J 1046. Received July 1997. which is used to establish that a system satis es certain properties, and equivalence or preorder relations (e.g. [9, 21, 22, 24]) which are used to establish that one system implements another, according to some notion of implementation. Each equivalence or preorder preserves some of the properties of a system, and thus the use of a relation as a notion of implementation means that we are interested only in the ....

....a strong bisimulation between M 1 and M 2 . 2 Condition 2 of De nition 11 is stated in [16] in a di erent but equivalent way, i.e. for each equivalence class [x] of R, the probabilities of reaching [x] from s 1 and s 2 are the same. Strong bisimulation coincides with the strong bisimulation of [22, 24] whenever the involved probabilistic automata represent ordinary automata. The next de nition is used to introduce strong simulations. A similar de nition appears in [13] Informally, 2 ; F 2 ; P 2 ) means that there is a way to split the probabilities of the states of 1 between the ....

Park, D.M.R. 1981. Concurrency and automata on in nite sequences. In 5 GI Conference, Volume 104 of Lecture Notes in Computer Science. SpringerVerlag, 167-183.

....methodology, as it seems to capture appropriately the black box character of data abstraction. This general notion instantiates to a behavioural equivalence of sequential programs or data types [Rei81, GGM76] as well as to the bisimulation equivalence (bisimilarity) of concurrent processes [Par81, Miln89]. Recently a categorical generalization of bisimulation was proposed, by means of open maps (open morphisms) JNW93] enabling a uniform de nition of bisimulation equivalence across a range of di erent models for parallel computations. This setting turned out appropriate for de ning, among ....

D.M.R. Park, Concurrency and Automata on In nite Sequences. Proc. 5th G.I. Conference, LNCS 104 (Springer-Verlag, 1981).

....overview) In particular, the nal coalgebra A satis es principles of coinduction, both for de nitions and for proofs. The latter are formulated in terms of socalled stream bisimulations , an elementary variation on Park s and Milner s original notion of bisimulation for parallel processes [Mil80, Par81]. As we shall see, these coinduction principles are surprisingly powerful. They will be applied to both data streams and time streams. Having modelled connector ends as timed data streams, we then model connectors as relations on timed data streams, expressing which combinations of timed data ....

....an immediate consequence of the de nition of bisimulation, we have R is a bisimulation , R (R) Bisimulation relations are, in other words, post xed points of . The characterisation of bisimulations as post xed points goes back, in the context of nondeterministic transition systems, to [Par81, Mil80]. Consequently, the coinduction proof principle (1) is equivalent to the following equality, where id = fh ; i j 2 A g: id = fR j R (R) g Since id is itself a (bisimulation and thus a) post xed point, it is in fact the greatest xed point of . Therefore the above ....

D.M.R. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Proceedings 5th GI conference, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer-Verlag, 1981.

....a type respecting relation R to closed terms. For a type respecting relation R we write R also for the induced relation on actions, given as the least congruence on actions so that u 1 7 a R u 2 7 a if u 1 R u 2 . 5. 1 Bisimulation A type respecting relation R on closed terms is a bisimulation [19, 21] if the following holds. If t 1 R t 2 , then 2 . Bisimilarity, is the largest bisimulation. Theorem 5. Bisimilarity is a congruence. Proof. We use Howe s method [11] as adapted to a typed setting by Gordon [9] In detail, we de ne the precongruence candidate ....

D. Park. Concurrency and automata on in nite sequences. In Proc. 5th GI Conference, LNCS 104, 1981.

....of algebras. There has been a spate of papers discussing coalgebraic versions of Birkho s theorem [29, 3, 17, 20, 23, 2, 15] This paper is concerned with covarieties that are closed under images of bisimulations, aptly named behavioural covarieties in [3] The original idea of a bisimulation [27, 26] was that of a binary relation of observational indistinguishability between states of two transition systems. States are hidden: all we observe is the behaviour of the system in response to inputs or other actions. States that cause the same behaviour are interchangeable, and so a computationally ....

David Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Theoretical Computer Science, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer-Verlag, 1981.

....of A is denoted by the state parameter s. The variable v takes values in A A, so 1 v and 2 v take values in A. Although v is free in these subterms, and indeed in the subterms beginning case size( j v) v is bound in M itself. M is rigid. The notion of a bisimulation rst appeared in [27] as a relation of mutual simulation between states of two automata. Park showed that if two deterministic automata are related by a bisimulation, then they accept the same set of inputs. Hennessy and Milner [12, 13] introduced the idea of characterising observationally equivalent, or behaviourally ....

David Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Theoretical Computer Science, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer-Verlag, 1981.

....of partial isomorphism is the building block of model equivalence. Since S4 u is multi modal language, one resorts to bisimulation, which is the modal analogue of partial isomorphism. Bisimulations compare models in a structured sense, just enough to ensure the truth of the same modal formulas [8, 13]. De nition 1 (Topological bisimulation) Given two topological models hX; O; i, hX i, a total topological bisimulation is a non empty relation X X de ned for all x 2 X and for all x such that if x x (base) x 2 (p) i x 2 (p) for any proposition letter p) ....

D. Park. Concurrency and Automata on In nite Sequences. In Proceedings of the 5th GI Conference, pages 167-183, Berlin, 1981. Springer Verlag.

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D. M. R. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, In Proc. of the 5th GI Conference, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer Verlag, 1989.

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D. Park. Concurrency and automata on in nite sequences. In 5th GI Conference on Theoretical Computer Science, pages 167-183. Lecture Notes in Comput. Sci. 184. Springer Verlag, 1981.

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D. Park. Concurrency and automata on in nite sequences. In Proc. 5th G-I Conference, vol. 104 of Lect. Notes in Comput. Sci., pages 167-183, Springer, 1981.

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D. Park. Concurrency and automata on in nite sequences. In Proceedings 5th GI-Conf. on Theoretical Computer Science, number 104 in LNCS, 1981. 25

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D. M. R. Park. Concurrency and Automata on In nite Sequences, volume 104 of LNCS. Springer, 1980.

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D.M.R. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Proceedings 5th GI Conference on Theoretical Computer Science, number 104 in Lect. Notes Comp. Sci., pages 15-32. Springer, Berlin, 1981.

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David Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Theoretical Computer Science, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer-Verlag, 1981.

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D. Park. Concurrency and automata on innite sequences. pages 561572. Springer Lect. Notes Comp. Sci. (104), 1981.

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D. Park. Concurrency and Automata on Innite Sequences. In P. Deussen, editor, 5th GI Conference, volume 104 of Lect. Notes in Comp. Sci. Springer, 1981.

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D. Park, Concurrency and automata on in nite sequences. LNCS 104 167-183 (1981).

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D. Park, Concurrency and automata on in#nite sequences, in: P. Deussen (Ed.), Proc. 5th GI Conf., Lecture Notes in Computer Science, vol. 104, Springer, Berlin, 1981, pp. 167--183.

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D. Park. Concurrency and automata on in nite sequences. In Proc. 5th GI Conference. Springer LNCS 104, 1981.

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David Park. Concurrency and automata on in nite sequences. In Peter Deussen, editor, Theoretical Computer Science: 5th GI-Conference, Karlsruhe, volume 104 of Lecture Notes in Computer Science, pages 167-183, Berlin, Heidelberg, and New York, March 1981. Springer-Verlag.

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D. M. R. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Theoretical Computer Science, pages 167-183. Springer, Berlin, 1981. LNCS 104.

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D. Park. Concurrency and automata on in nite sequences. In P. Deussen, editor, Fifth GI Conference on Theoretical Computer Science, volume 104 of Lecture Notes in Computer Science, pages 167-183. Springer-Verlag, 1981.

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