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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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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.
When Are Two Protocols the Same?
 Communication in MultiAgent Systems: Agent Communication Languages and Conversation Policies, Lecture Notes in Artificial Intelligence 2650
, 2002
"... A number of protocols based on the formal dialogue games of philosophy have recently been proposed for interactions between autonomous agents. Several of these proposals purport to assist agents engaged in the same types of interactions, such as persuasions and negotiations, and are superficially di ..."
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Cited by 23 (10 self)
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A number of protocols based on the formal dialogue games of philosophy have recently been proposed for interactions between autonomous agents. Several of these proposals purport to assist agents engaged in the same types of interactions, such as persuasions and negotiations, and are superficially different. How are we to determine whether or not these proposals are substantially different ? This paper considers this question and explores several alternative definitions of equivalence of protocols.
Relating StateBased and ProcessBased Concurrency through Linear Logic
, 2006
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
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Cited by 20 (3 self)
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired to Petri nets and multiset rewriting, and the prolific processbased models such as the πcalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic. In the second part of the paper, we propose a completely new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous πcalculus to rewrite operators, while the structural equivalence corresponds directly to logicallymotivated structural properties of ωmultisets (with one exception).
Big toy models: Representing physical systems as Chu spaces. Synthese, 2011. Online First, April 2011. Available as arXiv:0910.2393
 m,n 33 S. Abramsky. Relational Hidden Variables and NonLocality. Studia Logica
, 2012
"... We pursue a modeloriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we ..."
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We pursue a modeloriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a ‘big toy model’, in which both quantum and classical systems can be faithfully represented — as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces can be used to represent physical systems of various kinds. In particular, we show how quantum systems can be represented as Chu spaces over the unit interval in such a way that the Chu morphisms correspond exactly to the physically meaningful symmetries of the systems — the unitaries and antiunitaries. In this way we obtain a full and faithful functor from the groupoid of Hilbert spaces and their symmetries to Chu spaces. We also consider whether it is possible to use a finite value set rather than the unit interval; we show that three values suffice, while the two standard possibilistic reductions to two values both fail to preserve fullness. 1
EventState Duality: The Enriched Case
"... Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), a ..."
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Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), and partially ordered information systems.
Coalgebras, Chu Spaces, and Representations of Physical Systems
, 2009
"... We revisit our earlier work on the representation of quantum systems as Chu spaces, and investigate the use of coalgebra as an alternative framework. On the one hand, coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimu ..."
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We revisit our earlier work on the representation of quantum systems as Chu spaces, and investigate the use of coalgebra as an alternative framework. On the one hand, coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics.
The Glory of the Past and Geometrical Concurrency
"... This paper contributes to the general understanding of the geometrical model of concurrency that was named higher dimensional automata (HDAs) by Pratt and van Glabbeek. In particular we provide some understanding of the modal logics for such models and their expressive power in terms of the bisimula ..."
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This paper contributes to the general understanding of the geometrical model of concurrency that was named higher dimensional automata (HDAs) by Pratt and van Glabbeek. In particular we provide some understanding of the modal logics for such models and their expressive power in terms of the bisimulation that can be captured. The geometric model of concurrency is interesting from two main reasons: its generality and expressiveness, and the natural way in which autoconcurrency and action refinement are captured. Logics for this model, though, are not well investigated, where a simple, yet adequate, modal logic over HDAs was only recently introduced. As this modal logic, with two existential modalities, during and after, captures only split bisimulation, which is rather low in the spectrum of van Glabbeek and Vaandrager, the immediate question was what small extension of this logic could capture the more finegrained hereditary history preserving bisimulation (hh)? In response, the work in this paper provides several insights. One is the fact that the geometrical aspect of HDAs makes it possible to use for capturing the hhbisimulation, a standard modal logic that does not employ event variables, opposed to the two logics (over
Towards a Modeling Environment for Composing DomainSpecific Modeling Languages: A Case Study on Controlling Traffic Lights
"... Abstract. DomainSpecific Modeling Languages (DSMLs) play a fundamental syntax metamodeling enables the rapid and inexpensive development of DSMLs, the specification of DSML semantics is still a hard problem, particularly for models with heterogeneous models of computation. In this paper we consider ..."
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Abstract. DomainSpecific Modeling Languages (DSMLs) play a fundamental syntax metamodeling enables the rapid and inexpensive development of DSMLs, the specification of DSML semantics is still a hard problem, particularly for models with heterogeneous models of computation. In this paper we consider issues associated with creating modeling tools which allow for the composition of semantic units. Key concepts are shown through a very simple case study involving traffic controllers. Semantics for domainspecific modeling languages (DSMLs) can be specified in a number of ways according to the choices of the language designer, the concepts in the application domain, and the requirements of a particular application area. Semantics can also be used for various purposes in design and analysis. This suggests the need
Preliminary Proceedings of the Workshop on Geometry and Topology in Concurrency Theory
, 909
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Notes Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Notes Series publications. Copies may be obtained by contacting: BRICS