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43
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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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.
Homological properties of nondeterministic branchings and mergings in higher dimensional automata
 Homology, Homotopy and Applications
"... Abstract. The branching (resp. merging) space functor of a flow is a left Quillen functor. The associated derived functor allows to define the branching (resp. merging) homology of a flow. It is then proved that this homology theory is a dihomotopy invariant and that higher dimensional branchings (r ..."
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Cited by 13 (8 self)
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Abstract. The branching (resp. merging) space functor of a flow is a left Quillen functor. The associated derived functor allows to define the branching (resp. merging) homology of a flow. It is then proved that this homology theory is a dihomotopy invariant and that higher dimensional branchings (resp. mergings) satisfy a long exact sequence. Contents
A convenient category of locally preordered spaces
 Applied Categorical Structures
, 2008
"... Abstract. As a practical foundation for a homotopy theory of abstract spacetime, ..."
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Cited by 11 (0 self)
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Abstract. As a practical foundation for a homotopy theory of abstract spacetime,
Flow does not model flows up to weak dihomotopy
 Applied Categorical Structures
, 2005
"... In particular, a new approach of dihomotopy involving simplicial presheaves over an appropriate small category is proposed. This small category is obtained by taking a full subcategory of a locally presentable ..."
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Cited by 10 (4 self)
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In particular, a new approach of dihomotopy involving simplicial presheaves over an appropriate small category is proposed. This small category is obtained by taking a full subcategory of a locally presentable
Towards a homotopy theory of process algebra
 2008) 353–388 (electronic). MR2426108 (2009d:68115), Zbl 1151.68037
"... Abstract. This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebr ..."
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Abstract. This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebra with any synchronization algebra using a notion of labelled flow. This interpretation of process algebra satisfies the paradigm of higher dimensional automata: one nondegenerate full ndimensional cube (no more no less) in the underlying space of the time flow corresponding to the concurrent execution of n actions. This result will enable us in future papers to develop an homotopical approach of process algebras. Indeed, several homological constructions related to the causal structure of time flow are possible only in the framework of flows. Contents
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 7 (3 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
Combinatorics of labelling in higher dimensional automata
"... Abstract. The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled ncube, in exactly one way. The main ingredient is the nonfunctorial construction called labelled directed coskeleton. It i ..."
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Cited by 6 (1 self)
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Abstract. The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled ncube, in exactly one way. The main ingredient is the nonfunctorial construction called labelled directed coskeleton. It is defined as a subobject of the labelled coskeleton, the latter coinciding in the unlabelled case with the right adjoint to the truncation functor. This nonfunctorial construction is necessary since the labelled coskeleton functor of the category of labelled precubical sets does not fulfil the above requirement. We prove in this paper that it is possible to force the labelled coskeleton functor to be wellbehaved by working with labelled transverse symmetric precubical sets. Moreover, we prove that this solution is the only one. A transverse symmetric precubical set is a precubical set equipped with symmetry maps and with a new kind of degeneracy map called transverse degeneracy. Finally, we also prove that the two settings are equivalent from a directed algebraic topological viewpoint. To illustrate, a new semantics of CCS, equivalent to the old one, is given. Contents
Thomotopy and refinement of observation. IV. Invariance of the underlying . . .
, 2006
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Worytkiewicz: A model category for local pospaces
 Homology, Homotopy and Applications
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Dependently Typed Programming with DomainSpecific Logics
 SUBMITTED TO POPL ’09
, 2008
"... We define a dependent programming language in which programmers can define and compute with domainspecific logics, such as an accesscontrol logic that statically prevents unauthorized access to controlled resources. Our language permits programmers to define logics using the LF logical framework, ..."
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Cited by 6 (3 self)
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We define a dependent programming language in which programmers can define and compute with domainspecific logics, such as an accesscontrol logic that statically prevents unauthorized access to controlled resources. Our language permits programmers to define logics using the LF logical framework, whose notion of binding and scope facilitates the representation of the consequence relation of a logic, and to compute with logics by writing functional programs over LF terms. These functional programs can be used to compute values at runtime, and also to compute types at compiletime. In previous work, we studied a simplytyped framework for representing and computing with variable binding [LICS 2008]. In this paper, we generalize our previous type theory to account for dependently typed inference rules, which are necessary to adequately represent domainspecific logics, and we present examples of using our type theory for certified software and mechanized metatheory.