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Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 45 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
History Dependent Automata
, 2001
"... In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated i ..."
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Cited by 29 (8 self)
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In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the historypreserving semantics of Petri nets. Ordinary
Presheaf Models for the piCalculus
, 1997
"... Recent work has shown that presheaf categories provide a general model of concurrency, with an inbuilt notion of bisimulation based on open maps. Here it is shown how this approach can also handle systems where the language of actions may change dynamically as a process evolves. The example is the p ..."
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Cited by 12 (4 self)
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Recent work has shown that presheaf categories provide a general model of concurrency, with an inbuilt notion of bisimulation based on open maps. Here it is shown how this approach can also handle systems where the language of actions may change dynamically as a process evolves. The example is the picalculus, a calculus for `mobile processes' whose communication topology varies as channels are created and discarded. A denotational semantics is described for the picalculus within an indexed category of profunctors; the model is fully abstract for bisimilarity, in the sense that bisimulation in the model, obtained from open maps, coincides with the usual bisimulation obtained from the operational semantics of the picalculus. While attention is concentrated on the `late' semantics of the picalculus, it is indicated how the `early' and other variants can also be captured.
Types and Models for HigherOrder Action Calculi
, 1997
"... . Milner introduced action calculi as a framework for representing models of interactive behaviour. He also introduced the higherorder action calculi, which add higherorder features to the basic setting. We present type theories for action calculi and higherorder action calculi, and give the categ ..."
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Cited by 6 (5 self)
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. Milner introduced action calculi as a framework for representing models of interactive behaviour. He also introduced the higherorder action calculi, which add higherorder features to the basic setting. We present type theories for action calculi and higherorder action calculi, and give the categorical models of the higherorder calculi. As applications, we give a semantic proof of the conservativity of higherorder action calculi over action calculi, and a precise connection with Moggi's computational lambda calculus and notions of computation. 1 Introduction Milner introduced action calculi as a framework for representing models of interactive behaviour [Mil96]. He also introduced two conservative extensions: higherorder action calculi [Mil94a], which add higherorder features to the basic setting, and reflexive action calculi [Mil94b], which give recursion in the presence of the higherorder features. Various examples, which explore the role of action calculi as a general frame...
A πcalculus process semantics of concurrent idealised ALGOL
 In Proc. FOSSACS'99, volume 1578 of LNCS
, 1999
"... We study the use of the πcalculus for semantical descriptions of languages such as Concurrent Idealised ALGOL (CIA), combining imperative, functional and concurrent features. We first present an operational semantics for CIA, given by SOS rules and a contextual form of behavioural equivalence; th ..."
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Cited by 3 (0 self)
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We study the use of the πcalculus for semantical descriptions of languages such as Concurrent Idealised ALGOL (CIA), combining imperative, functional and concurrent features. We first present an operational semantics for CIA, given by SOS rules and a contextual form of behavioural equivalence; then a πcalculus semantics. As behavioural equivalence on πcalculus processes we choose the standard (weak early) bisimilarity. We compare the two semantics, demonstrating that there is a close operational correspondence between them and that the πcalculus semantics is sound. This allows for applying thecalculus theory in proving behavioural properties of CIA phrases. We discuss laws and examples which have served as benchmarks to various semantics, and a more complex example involving procedures of higher order.
Final Semantics for the picalculus
, 1998
"... In this paper we discuss final semantics for the calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the final semantics paradigm, originated by Aczel and Rutten for CCSlike languages, can be successfully applied also here. This i ..."
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Cited by 2 (2 self)
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In this paper we discuss final semantics for the calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the final semantics paradigm, originated by Aczel and Rutten for CCSlike languages, can be successfully applied also here. This is achieved by suitably generalizing the standard techniques so as to accommodate the mechanism of name creation and the behaviour of the binding operators peculiar to the calculus. As a preliminary step, we give a higher order presentation of the calculus using as metalanguage LF , a logical framework based on typed calculus. Such a presentation highlights the nature of the binding operators and elucidates the role of free and bound channels. The final semantics is defined making use of this higher order presentation, within a category of hypersets.
Structured Coalbegras and Minimal HDAutomata for the πCalculus
, 2000
"... The coalgebraic framework developed for the classical process algebras, and in particular its advantages concerning minimal realizations, does not fully apply to the picalculus, due to the constraints on the freshly generated names that appear in the bisimulation. In this paper we propose to model ..."
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The coalgebraic framework developed for the classical process algebras, and in particular its advantages concerning minimal realizations, does not fully apply to the picalculus, due to the constraints on the freshly generated names that appear in the bisimulation. In this paper we propose to model the transition system of the πcalculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a category. We show that permutations are sufficient to represent in an explicit way fresh name generation, thus allowing for the definition of minimal realizations. We also link the coalgebraic semantics with a slightly improved version of history dependent (HD) automata, a model developed for verification purposes, where states have local names and transitions are decorated with names and name relations. HDautomata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized. We show that the bisimulation relation in the coalgebraic context corresponds to the minimal HDautomaton.