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On the Expressiveness of higher dimensional automata
 EXPRESS 2004, ENTCS
, 2005
"... Abstract In this paper I compare the expressive power of several models of concurrency based on their ability to represent causal dependence. To this end, I translate these models, in behaviour preserving ways, into the model of higher dimensional automata, which is the most expressive model under i ..."
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Cited by 29 (0 self)
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Abstract In this paper I compare the expressive power of several models of concurrency based on their ability to represent causal dependence. To this end, I translate these models, in behaviour preserving ways, into the model of higher dimensional automata, which is the most expressive model under investigation. In particular, I propose four different translations of Petri nets, corresponding to the four different computational interpretations of nets found in the literature. I also extend various equivalence relations for concurrent systems to higher dimensional automata. These include the history preserving bisimulation, which is the coarsest equivalence that fully respects branching time, causality and their interplay, as well as the STbisimulation, a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time. Through their embeddings in higher dimensional automata, it is now welldefined whether members of different models of concurrency are equivalent.
HOMOTOPICAL INTERPRETATION OF GLOBULAR COMPLEX BY MULTIPOINTED DSPACE
"... Abstract. Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a ..."
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Cited by 10 (4 self)
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Abstract. Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is equivalent to the homotopy category of flows. The underlying
Inverting weak dihomotopy equivalence using homotopy continuous flow
 Theory Appl. Categ
"... Abstract. A flow is homotopy continuous if it is indefinitely divisible up to Shomotopy. The full subcategory of cofibrant homotopy continuous flows has nice features. Not only it is big enough to contain all dihomotopy types, but also a morphism between them is a weak dihomotopy equivalence if and ..."
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Cited by 6 (4 self)
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Abstract. A flow is homotopy continuous if it is indefinitely divisible up to Shomotopy. The full subcategory of cofibrant homotopy continuous flows has nice features. Not only it is big enough to contain all dihomotopy types, but also a morphism between them is a weak dihomotopy equivalence if and only if it is invertible up to dihomotopy. Thus, the category of cofibrant homotopy continuous flows provides an implementation of Whitehead’s theorem for the full dihomotopy relation, and not only for Shomotopy as in previous works of the author. This fact is not the consequence of the existence of a model structure on the category of flows because it is known that there does not exist any model structure on it whose weak equivalences are exactly the weak dihomotopy equivalences. This fact is an application of a general result for the localization of a model category with respect to a weak factorization system. Contents
RELATIVE DIRECTED HOMOTOPY THEORY OF PARTIALLY ORDERED SPACES
"... Algebraic topological methods have been used successfully in concurrency theory, the domain of theoretical computer science that deals with parallel computing. L. Fajstrup, E. Goubault, and M. Raussen have introduced partially ordered spaces (pospaces) as a model for concurrent systems. In this pape ..."
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Algebraic topological methods have been used successfully in concurrency theory, the domain of theoretical computer science that deals with parallel computing. L. Fajstrup, E. Goubault, and M. Raussen have introduced partially ordered spaces (pospaces) as a model for concurrent systems. In this paper it is shown that the category of pospaces under a fixed pospace is both a fibration and a cofibration category in the sense of H. Baues. The homotopy notion in this fibration and cofibration category is relative directed homotopy. It is also
Abstract On the Expressiveness of Higher Dimensional Automata
"... In this paper I compare the expressive power of several models of concurrency based on their ability to represent causal dependence. To this end, I translate these models, in behaviour preserving ways, into the model of higher dimensional automata, which is the most expressive model under investigat ..."
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In this paper I compare the expressive power of several models of concurrency based on their ability to represent causal dependence. To this end, I translate these models, in behaviour preserving ways, into the model of higher dimensional automata, which is the most expressive model under investigation. In particular, I propose four different translations of Petri nets, corresponding to the four different computational interpretations of nets found in the literature. I also extend various equivalence relations for concurrent systems to higher dimensional automata. These include the history preserving bisimulation, which is the coarsest equivalence that fully respects branching time, causality and their interplay, as well as the STbisimulation, a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time. Through their embeddings in higher dimensional automata, it is now welldefined whether members of different models of concurrency are equivalent.
Contents
, 2004
"... Abstract. A functor is constructed from the category of globular CWcomplexes to that of flows. It allows to compare the Shomotopy equivalences (resp. the Thomotopy equivalences) of globular complexes with the Shomotopy equivalences (resp. the Thomotopy equivalences) of flows. Moreover, one prov ..."
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Abstract. A functor is constructed from the category of globular CWcomplexes to that of flows. It allows to compare the Shomotopy equivalences (resp. the Thomotopy equivalences) of globular complexes with the Shomotopy equivalences (resp. the Thomotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular CWcomplexes with respect to Shomotopy equivalences to the localization of the category of flows with respect to weak
THOMOTOPY AND REFINEMENT OF OBSERVATION (I): Introduction
, 2005
"... This paper is the extended introduction of a series of papers about modelling Thomotopy by refinement of observation. The notion of Thomotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other construction in ..."
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This paper is the extended introduction of a series of papers about modelling Thomotopy by refinement of observation. The notion of Thomotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other construction in
Homotopical interpretation of globular . . .
, 2007
"... Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a combinat ..."
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Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is