G.L. Cattani and V. Sassone. Higher dimensional transition systems. In 11  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Hhp bisimilarity appears to be only a slight strengthening of hp bisimilarity [15] and hence many attempts have been made to extend the above mentioned algorithms to the case of hhp bisimilarity. However, decidability of hhp bisimilarity has remained open, despite several attempts over the years [22, 23, 3, 7]. Fr oschle and Hildebrandt [7] have discovered an in nite hierarchy of bisimilarity notions re ning hp bisimilarity, and coarser than hhp bisimilarity, such that hhp bisimilarity is the intersection of all the bisimilarities in the hierarchy. They have shown all these bisimilarities to be ....

Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems. In Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, pages 55-62, New Brunswick, New Jersey, 27-30 July 1996. IEEE Computer Society Press.

....For instance, when possible (basically, you should check that you are not in the situation of Figure 1) one replaces an interleaving square of two actions by the transition s 0 fa;bg s 3 . This is obviously subsumed by our notion of n transition (formally, this can be done in the style of [39]) Algorithmics of the representation of the state space. A number of clever algorithmic methods have been used to reduce the representation of the state space in memory without discarding any transition nor state, rather by compressing the representation. A very much used technique in ....

V. Sassone and G. L. Cattani. Higher-dimensional transition systems. In Proceedings of LICS'96, 1996.

....that monoidal categories provide a superior model of net behaviour. To illustrate better the differences between the two semantic frameworks above, we adopt concurrent transition systems as a bridge model. These are a much simplified, deterministic version of higher dimensional transition systems [3] that we select as the simplest one able to convey our ideas. Concurrent transition systems resemble configuration structures, but are more expressive. They also draw on earlier very significant models, such as distributed transition systems [9] step and PN transition systems [16] and local ....

....without allowing this to determine the set of transitions completely. Several such models appear in the literature. Among those that inspired us most, we recall distributed transition systems [9] step transition systems [16] PN transition systems [16] and higher dimensional transition systems [3]. Also closely related are the local event structures of [8] a model that extends event structures (rather than transition systems) by allowing the firing of sets (but not multisets) of events. Drawing on all these, we have here chosen the simplest definition that suits our current aim. ....

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G.L. CATTANI AND V. SASSONE (1996), Higher Dimensional Transition Systems, in Proceedings of the 11th Symposium on Logics in Computer Science, 55--62, IEEE Press.

.... and Labelled Asynchronous Transition Systems Several e#orts have been devoted to the search for independence models based on the model of (labelled) transition systems, e.g. transition systems enriched with additional features that make expressing concurrency explicitly possible (cf. e.g. [111, 130, 50, 51, 133, 20]) An important motivation is to find models suitable for giving structural operational semantics to e.g. process calculi that takes independence information into account. The work in Ch. 4 and Ch. 5 investigate the formal relationship between two similar approaches, respectively the model of ....

.... checking system properties such as safety properties and fairness [46, 129, 105] Several e#orts have been devoted to the search of transition based noninterleaving models, e.g. transition systems enriched with additional features that make expressing concurrency explicitly possible (cf. e.g. [111, 130, 50, 51, 133, 20]) The present paper focuses on two such models, namely asynchronous transition systems, introduced independently by Bednarczyk [11] and Shields [122] and transitions systems with independence, proposed by Winskel and Nielsen [146] These two competing approaches are, among the others, those ....

Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems. In LICS'96. IEEE, 1996.

....Hhp bisimilarity appears to be only a slight strengthening of hp bisimilarity [JNW96] and hence many attempts have been made to extend the above mentioned algorithms to the case of hhp bisimilarity. However, decidability of hhpbisimilarity has remained open, despite several attempts over the years [NC95, NW96, CS96, FH99]. Fr oschle and Hildebrandt [FH99] have discovered an in nite hierarchy of bisimilarity notions re ning hp bisimilarity, and coarser than hhp bisimilarity, such that hhp bisimilarity is the intersection of all the bisimilarities in the hierarchy. They have shown all these bisimilarities to be ....

Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems. In Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, pages 55-62, New Brunswick, New Jersey, 27{ 30 July 1996. IEEE Computer Society Press.

....morphisms have a path lifting property that we believe would be in higher dimensional transition systems a (geometric) fibration property. We thus hope that homotopy invariants could be useful for the study of a variety of bisimulation equivalences. Some work has been done in that direction in [25] (and in some sense also in [16] ....

V. Sassone and G. L. Cattani. Higher-dimensional transition systems. In Proceedings of LICS'96, 1996.

.... of the work of one of the co authors, 26] 27] 32] and also [45] Also there are links with the homological considerations of [23] and [24] Some potentially related semantic models are the n categorical formulations of [9] and some other combinatorial or categorical formulations in [21] [52], 55] 56] 57] In program analysis, some proposals have been made to use the scheduling information that one can extract from the geometry of executions, to derive automatic parallelization algorithms. This has been hinted in [28] where some other ideas for program analysis are exemplified) ....

V. Sassone and G. L. Cattani, Higher-dimensional transition systems, Proceedings of LICS'96, 1996.

....Hhp bisimilarity seems to be only a slight strengthening of hp bisimilarity [12] and hence many attempts have been made to extend the above mentioned algorithms to the case of hhp bisimilarity. However, decidability of hhp bisimilarity has remained open, despite several attempts over the years [17,18,2,5]. Froschle and Hildebrandt [5] have discovered an infinite hierarchy of bisimilarity notions refining hp bisimilarity, and coarser than hhp bisimilarity, such that hhpbisimilarity is the intersection of all the bisimilarities in the hierarchy. They have shown all these bisimilarities to be ....

Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems. In Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, pages 55--62, New Brunswick, New Jersey, 27--30 July 1996. IEEE Computer Society Press.

....geometric model of concurrency, refining this approach by not necessarily filling in all squares and cubes, but explicitly filling in only those that one wants to represent concurrency. Alternative formalisations of this idea appear in Van Glabbeek [8] Goubault Jensen [11] and Cattani Sassone [4]. Although the resulting model of 4 higher dimensional automata is more complicated than that of plain automata or process graphs, it is more expressive as well. The Petri net below, for infflffl a ffl b ffl c ffl a b c b c b a c a c a b stance, is expressible by a higher ....

G.L. Cattani & V. Sassone (1996): Higher dimensional transition systems. In Proceedings 11 th Annual IEEE Symposium on Logic in Computer Science (LICS 96), New Brunswick, USA, IEEE Computer Society Press, pp. 55--62.

....to be a rather innocent strengthening of hp bisimilarity, and hence many attempts have been made to extend the above mentioned algorithms to the case of hhp bisimilarity. However, decidability of hhp bisimilarity has remained open ever since its inception, despite several attempts over the years [NC95, NW96, CS96, FH99]. Froschle and Hildebrandt [FH99] have discovered an infinite hierarchy of bisimilarity notions refining hp bisimilarity, and coarser than hhp bisimilarity, such that hhp bisimilarity is the intersection of all the bisimilarities in the hierarchy. They have shown all these bisimilarities to be ....

Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems. In Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, pages 55--62, New Brunswick, New Jersey, 27--30 July 1996. IEEE Computer Society Press.

.... b ffl a ffl a b : 1) 4 Several efforts have been devoted to the search of transition based noninterleaving models, e.g. transition systems enriched with additional features that make expressing concurrency explicitly possible (cf. e.g. [Pra91, vG, Gou93, GJ92, vGP95, CS96]) We have focused on two such models, namely asynchronous transition systems, introduced independently by Bednarczyk [Bed88] and Shields [Shi85] and transitions systems with independence, proposed by Winskel and Nielsen [WN94] These two approaches are, among the others, those building on the ....

G.-L. Cattani and V. Sassone. Higher dimensional transition systems. In Proc. LICS '96. IEEE, 1996.

....be available. This might help in settling our first conjecture (see Section 3, x Complete cuboidal sets) which is important for our representation programme. At a more speculative level, we wonder what the relationship is between this work and presheaf or higherdimensional models of concurrency [23, 42, 6, 41, 19, 18, 5, 20]. ....

G.L. Cattani and V. Sassone. Higher dimensional transition systems. In 11 th LICS Conf., pages 55-- 62. IEEE, Computer Society Press, 1996.

.... from other models such as event structures, asynchronous transition systems and higher dimensional transition systems which come equipped with a mechanism for expressing opportunities for concurrency but where that mechanism is inconsistent with the opportunities which arise from forming products [43,11]. Conventional transition systems have a start state. By analogy a pointed graph is a pair (J; O J : 1 J) for some graph J . The category of pointed graphs is the comma category O RGrph = 1 # RGrph. The required functor to Cat simply forgets the point and forms the free category. The language ....

Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 55--62. IEEE Computer Society Press, 1996.

.... of the work of one of the co authors, 27] 28] 33] and also [46] Also there are links with the homological considerations of [24] and [25] Some potentially related semantic models are the n categorical formulations of [10] and some other combinatorial or categorical formulations in [22] [53], 56] 57] 58] In program analysis, some proposals have been made to use the scheduling information that one can extract from the geometry of executions, to derive automatic parallelization algorithms. This has been hinted in [29] where some other ideas for program analysis are exemplified) ....

V. Sassone and G. L. Cattani, Higher-dimensional transition systems, Proceedings of LICS'96, 1996.

.... causality in proof nets related to some standard proof theoretic results, like the sequentialisation theorem and the token games of [2] Moreover, like in L , actions are multisets of terminal formulas, and we are approximating true concurrency by means of a higherdimensional transition system [8]. The extension of this results to the full language constitutes work in progress. 8 Related Work and Conclusion In the present paper, we presented a compositional semantics for a concurrent programming language based in linear logic organized around the theory of proof nets. Proof nets have been ....

G. L. Cattani and V. Sassone. Higher dimensional transition systems. In Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 55-- 62. IEEE Computer Society Press, 1996.

....that monoidal categories provide a superior model of net behaviour. To illustrate better the differences between the two semantic frameworks above, we adopt concurrent transition systems as a bridge model. These are a much simplified, deterministic version of higher dimensional transition systems [3] that we select as the simplest one able to convey our ideas. Concurrent transition systems resemble configuration structures, but are more expressive. They also draw on earlier very significant models, such as distributed transition systems [9] step and PN transition systems [16] and local ....

....without allowing this to determine the set of transitions completely. Several such models appear in the literature. Among those that inspired us most, we recall distributed transition systems [9] step transition systems [16] PN transition systems [16] and higher dimensional transition systems [3]. Also closely related are the local event structures of [8] a model that extends event structures (rather than transition systems) by allowing the firing of sets (but not multisets) of events. Drawing on all these, we have here chosen the simplest definition that suits our current aim. ....

[Article contains additional citation context not shown here]

G.L. CATTANI AND V. SASSONE (1996), Higher Dimensional Transition Systems, in Proceedings of the 11th Symposium on Logics in Computer Science, 55--62, IEEE Press.

....and event structures are both attractive models of concurrency, raising the question of whether their respective intuitions about the nature of concurrency are compatible. Second, HDA s and event structures draw on complementary areas of mathematics: much of the HDA work since its introduction [vG96, GJ92, GC93, Gou93, Gun94, Gou95b, Gou95a, Gou96a, Gou96b, BJ96, SC96, Tak96] has drawn on methods in algebraic topology, in particular homotopy and homology, whereas event structures tend to depend more on methods from domain theory and logic, especially those involving duality. It is therefore both intrinsically interesting in principle and important in practice for ....

V. Sassone and G. L. Cattani. Higher-dimensional transition systems. In Proceedings of LICS'96, 1996.

.... based on n categories as models of higher dimensional automata is introduced, but the modelling power obtained does not seem to be greater than that of ordinary PT nets, though the framework is highly elegantly linked to algebraic topology (Goubault and Jensen 1992; Goubault 1993; see also Cattani and Sassone 1996), Hoogers et al. 1992) in which the authors give semantics to PT nets in terms of generalized trace languages and discuss how using their work it could perhaps be possible to obtain a concept of unfolding for PT nets; and (Engelfriet 1991) where the unfolding of Petri nets is given in term of a ....

Cattani, G-L. and Sassone, V. (1996) Higher Dimensional Transition Systems. In Proceedings of the 11th LICS Symposium, IEEE Press, to appear.

....provides a means to solve certain mutual exclusion and atomicity problems (e.g. the dining philosopher P j . f(a) f(b) e(a; b) that must acquire both forks before he can start eating: in L , the agent (f(a) P; f(b) can reduce but to e(a; b) Multiset actions where also used recently by [6] in the definition higher dimensional transition systems, a generalisation of transition systems approximating true concurrent operational semantics. Substitution application can be extended to actions in the expected way, that is, oe(ft 1 ; Delta Delta Delta ; t n g) foe(t 1 ) Delta Delta ....

G. L. Cattani and V. Sassone. Higher dimensional transition systems. In Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 55--62. IEEE Computer Society Press, 1996.

....with Vladimiro Sassone [23] we introduced a new category of models for concurrency building on previous intuitions of Pratt [112] and van Glabbeek [40] Open maps were used to give an abstract characterisation of the notion of bisimulation that we had devised. The step further that we are making [24] is that of harnessing the machinery presented in Chapter 3 of this thesis for the purpose of the semantics of concurrent processes as hdts. In this way we expect to obtain automatically congruence results for bisimulation. Hdts seem also appropriate for modelling so called coordination languages ....

Gian Luca Cattani and Vladimiro Sassone. On higher dimensional transition systems. Manuscript in preparation, 1998.

....9.2 Further research There are several lines for future research, extending the work presented here. We briefly outline here some of the possibilities as well as some connections with related research. 9.2. 1 Higher dimensional transition systems (hdts) In a joint work with Vladimiro Sassone [23] we introduced a new category of models for concurrency building on previous intuitions of Pratt [112] and van Glabbeek [40] Open maps were used to give an abstract characterisation of the notion of bisimulation that we had devised. The step further that we are making [24] is that of harnessing ....

Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems.

.... checking system properties such as safety [8] and liveness properties [21, 17] Several efforts have been devoted to the search of transition based noninterleaving models, e.g. transition systems enriched with additional features that make expressing concurrency explicitly possible (cf. e.g. [18, 4, 6, 7, 5, 3]) The present paper focuses on two such models, namely asynchronous transition systems, introduced independently by Bednarczyk [1] and Shields [20] and transitions systems with independence, proposed by Winskel and Nielsen [22] These two competing approaches are, among the others, those ....

G. CATTANI AND V. SASSONE, Higher Dimensional Transition Systems, Proceedings of LICS'96, IEEE Computer Society Press (####), ##--##.

....symmetric monoidal categories provide a superior model of net behavior. To better illustrate the differences between the two semantic frameworks mentioned above, we adopt concurrent transition systems as a bridge model. These are a much simplified version of higher dimensional transition systems [9] that we choose as the simplest bridge model that can best convey our ideas. Concurrent transition systems resemble configuration structures, but they are more expressive. They also draw on earlier very significant models, such as distributed transition systems [18] step and PN transition ....

....without allowing this to determine the set of transitions completely. Several such models appear in the literature. Among those that inspired us most, we recall distributed transition systems [18] step transition systems [26] PN transition systems [26] and higher dimensional transition systems [9]. Also closely 16 BRUNI, MESEGUER, MONTANARI AND SASSONE related are the local event structures of [17] a model that extends event structures (rather than transition systems) by allowing the firing of sets (but not multisets) of events. Drawing on all these, we have here chosen the simplest ....

[Article contains additional citation context not shown here]

G.L. Cattani and V. Sassone (1996), Higher Dimensional Transition Systems, in Proceedings of the 11th Symposium on Logics in Computer Science, 55--62, IEEE Press.

.... checking system properties such as safety properties and fairness [8, 20, 16] Several efforts have been devoted to the search of transition based noninterleaving models, e.g. transition systems enriched with additional features that make expressing concurrency explicitly possible (cf. e.g. [17, 4, 6, 7, 5, 3]) The present paper focuses on two such models, namely asynchronous transition systems, introduced independently by Bednarczyk [1] and Shields [19] and transitions systems with independence, proposed by Winskel and Nielsen [21] These two competing approaches are, among the others, those ....

G-L. Cattani and V. Sassone. Higher Dimensional Transition Systems, To appear in Proceedings of LICS 96 (1996), IEEE Computer Society Press.

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G.L. Cattani and V. Sassone. Higher dimensional transition systems. In 11

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