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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
Optimal Purely Functional Priority Queues
 JOURNAL OF FUNCTIONAL PROGRAMMING
, 1996
"... Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert, and meld in O(1) worstcase time, and deleteMin in O(log n) worstcase time. These bounds are asymptotically optimal among all comparisonbased priority queues. In this paper, we adapt B ..."
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Cited by 18 (1 self)
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Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert, and meld in O(1) worstcase time, and deleteMin in O(log n) worstcase time. These bounds are asymptotically optimal among all comparisonbased priority queues. In this paper, we adapt Brodal's data structure to a purely functional setting. In doing so, we both simplify the data structure and clarify its relationship to the binomial queues of Vuillemin, which support all four operations in O(log n) time. Specifically, we derive our implementation from binomial queues in three steps: first, we reduce the running time of insert to O(1) by eliminating the possibility of cascading links; second, we reduce the running time of findMin to O(1) by adding a global root to hold the minimum element; and finally, we reduce the running time of meld to O(1) by allowing priority queues to contain other priority queues. Each of these steps is expressed using MLstyle functors. The last transformation, known as datastructural bootstrapping, is an interesting application of higherorder functors and recursive structures.
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.
Profunctors, open maps and bisimulation
 Mathematical Structures in Computer Science, To appear. Available from the Glynn Winskel’s web
, 2000
"... ..."
Objects as Mobile Processes
 RESEARCH SERIES RS9638, BRICS
, 1996
"... The object calculus of Abadi and Cardelli [AC96, AC94b, AC94a] is intended as model of central aspects of objectoriented programming languages. In this paper we encode the object calculus in the asynchronous picalculus without matching and investigate the properties of our encoding. ..."
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Cited by 11 (4 self)
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The object calculus of Abadi and Cardelli [AC96, AC94b, AC94a] is intended as model of central aspects of objectoriented programming languages. In this paper we encode the object calculus in the asynchronous picalculus without matching and investigate the properties of our encoding.
The Fixpoint BoundedVariable Queries are PSPACEComplete
 Presented at the 10th Annual International Conference of the European Association for Computer Science Logic, CSL '96
, 1996
"... We study complexity of the evaluation of fixpoint boundedvariable queries in relational databases. We exhibit a finite database such that the problem whether a closed fixpoint formula using only 2 individual variables is satisfied in this database is PSPACEcomplete. This clarifies the issues ra ..."
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Cited by 7 (0 self)
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We study complexity of the evaluation of fixpoint boundedvariable queries in relational databases. We exhibit a finite database such that the problem whether a closed fixpoint formula using only 2 individual variables is satisfied in this database is PSPACEcomplete. This clarifies the issues raised by Moshe Vardi in [Var95]. We study also the complexity of query evaluation for a number of restrictions of fixpoint logic. In particular we exhibit a sublogic for which the upper bound postulated by Vardi holds.
Categorical Models for Concurrency: Independence, Fairness and Dataflow
 BRICS DISSERTATION SERIES DS001
, 2000
"... This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing t ..."
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Cited by 6 (4 self)
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This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of different and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency. The work
Basic Research in Computer Science
, 2004
"... This paper studies fundamental connections between profunctors (i.e., distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Cons ..."
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This paper studies fundamental connections between profunctors (i.e., distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Consequently, the composition of profunctors preserves open maps as 2cells. A guiding idea is the view that profunctors, and colimit preserving functors, are linear maps in a model of classical linear logic. But profunctors, and colimit preserving functors, as linear maps, are too restrictive for many applications. This leads to a study of a range of pseudocomonads and how nonlinear maps in their coKleisli bicategories preserve open maps and bisimulation. The pseudocomonads considered are based on finite colimit completion, "lifting", and indexed families.
Contents
, 2013
"... Abstract. In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent presheaf semantics and as a concurrent game semantics. It is here proved that a behavioural equivalence induced by this semantics on CCS processes is fully abstract for fair testing equivalen ..."
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Abstract. In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent presheaf semantics and as a concurrent game semantics. It is here proved that a behavioural equivalence induced by this semantics on CCS processes is fully abstract for fair testing equivalence. The proof relies on a new algebraic notion called playground, which represents the ‘rule of the game’. From any playground, two languages, equipped with labelled transition systems, are derived, as well as a strong, functional