Results 1  10
of
28
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
Abstract

Cited by 304 (36 self)
 Add to MetaCart
The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
2011): Nominal terms and nominal logics: from foundations to metamathematics
 In: Handbook of Philosophical Logic
"... ABSTRACT: Nominal techniques concern the study of names using mathematical semantics. Whereas in much previous work names in abstract syntax were studied, here we will study them in metamathematics. More specifically, we survey the application of nominal techniques to languages for unification, rew ..."
Abstract

Cited by 15 (9 self)
 Add to MetaCart
(Show Context)
ABSTRACT: Nominal techniques concern the study of names using mathematical semantics. Whereas in much previous work names in abstract syntax were studied, here we will study them in metamathematics. More specifically, we survey the application of nominal techniques to languages for unification, rewriting, algebra, and firstorder logic. What characterises the languages of this chapter is that they are firstorder in character, and yet they can specify and reason on names. In the languages we develop, it will be fairly straightforward to give firstorder ‘nominal ’ axiomatisations of namerelated things like alphaequivalence, captureavoiding substitution, beta and etaequivalence, firstorder logic with its quantifiers—and as we shall see, also arithmetic. The formal axiomatisations we arrive at will closely resemble ‘natural behaviour’; the specifications we see typically written out in normal mathematical usage. This is possible because of a novel namecarrying semantics in nominal sets, through which our languages will have namepermutations and termformers that can bind as primitive builtin features.
Event Structures with Symmetry
 GDP FESTSCHRIFT, ENTCS, TO APPEAR
"... A category of event structures with symmetry is introduced and its categorical properties investigated. Applications to the eventstructure semantics of higher order processes, nondeterministic dataflow and the unfolding of Petri nets with multiple tokens are sketched. ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
A category of event structures with symmetry is introduced and its categorical properties investigated. Applications to the eventstructure semantics of higher order processes, nondeterministic dataflow and the unfolding of Petri nets with multiple tokens are sketched.
Probability, Nondeterminism and Concurrency: Two Denotational Models for Probabilistic Computation
 PHD THESIS, UNIV. AARHUS, 2003. BRICS DISSERTATION SERIES
, 2003
"... Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particular t ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particular there is no categorical distributive law between them. We introduce the powerdomain of indexed valuations which modifies the usual probabilistic powerdomain to take more detailed account of where probabilistic choices are made. We show the existence of a distributive law between the powerdomain of indexed valuations and the nondeterministic powerdomain. By means of an equational theory we give an alternative characterisation of indexed valuations and the distributive law. We study the relation between valuations and indexed valuations. Finally we use indexed valuations to give a semantics to a programming language. This semantics reveals the computational intuition lying behind the mathematics. In the second part of the thesis we provide an operational reading of continuous valuations on certain domains (the distributive concrete domains of Kahn and Plotkin) through the model of probabilistic event structures. Event structures are a model for concurrent computation that account for causal relations between events. We propose a way of adding probabilities to confusion free event structures, defining the notion of probabilistic event structure. This leads to various ideas of a run for probabilistic event structures. We show a confluence theorem for such runs. Configurations of a confusion free event structure form a distributive concrete domain. We give a representation theorem which characterises completely the powerdomain of valuations of such concrete domains in terms of prob...
Events, Causality and Symmetry
, 2008
"... The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences, actual and potential, are discussed.
1 Turing Machines with Atoms
"... Abstract—We study Turing machines over sets with atoms, also known as nominal sets. Our main result is that deterministic machines are weaker than nondeterministic ones; in particular, P=NP in sets with atoms. Our main construction is closely related to the CaiFürerImmerman graphs used in descript ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
Abstract—We study Turing machines over sets with atoms, also known as nominal sets. Our main result is that deterministic machines are weaker than nondeterministic ones; in particular, P=NP in sets with atoms. Our main construction is closely related to the CaiFürerImmerman graphs used in descriptive complexity theory. I.
NewHOPLA— A HigherOrder Process Language with Name Generation
, 2004
"... 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 Report Series publications. Copies may be obtained by contacting: BRICS ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
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 Report Series publications. Copies may be obtained by contacting: BRICS
Stone duality for nominal Boolean algebras with NEW
 In Proceedings of the 4th international conference on algebra and coalgebra in computer science (CALCO 2011), volume 6859 of Lecture Notes in Computer Science
, 2011
"... Abstract. We define Boolean algebras over nominal sets with a functionsymbol Nmirroring the N‘fresh name ’ quantifier. We also define dual notions of nominal topology and Stone space, prove a representation theorem over fields of nominal sets, and extend this to a Stone duality. 1 ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We define Boolean algebras over nominal sets with a functionsymbol Nmirroring the N‘fresh name ’ quantifier. We also define dual notions of nominal topology and Stone space, prove a representation theorem over fields of nominal sets, and extend this to a Stone duality. 1
Investigations into Algebra and Topology over Nominal Sets
, 2011
"... The last decade has seen a surge of interest in nominal sets and their applications to formal methods for programming languages. This thesis studies two subjects: algebra and duality in the nominal setting. In the first part, we study universal algebra over nominal sets. At the heart of our approach ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
The last decade has seen a surge of interest in nominal sets and their applications to formal methods for programming languages. This thesis studies two subjects: algebra and duality in the nominal setting. In the first part, we study universal algebra over nominal sets. At the heart of our approach lies the existence of an adjunction of descent type between nominal sets and a category of manysorted sets. Hence nominal sets are a full reflective subcategory of a manysorted variety. This is presented in Chapter 2. Chapter 3 introduces functors over manysorted varieties that can be presented by operations and equations. These are precisely the functors that preserve sifted colimits. They play a central role in Chapter 4, which shows how one can systematically transfer results of universal algebra from a manysorted variety to nominal sets. However, the equational logic obtained is more expressive than the nominal equational logic of Clouston and Pitts, respectively, the nominal algebra of Gabbay and Mathijssen. A uniform fragment of our logic with the same expressivity