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17
Freshregister automata
 In Proceedings of the 38th Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages (POPL ’11
, 2011
"... What is a basic automatatheoretic model of computation with names and freshname generation? We introduce FreshRegister Automata (FRA), a new class of automata which operate on an infinite alphabet of names and use a finite number of registers to store fresh names, and to compare incoming names wi ..."
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What is a basic automatatheoretic model of computation with names and freshname generation? We introduce FreshRegister Automata (FRA), a new class of automata which operate on an infinite alphabet of names and use a finite number of registers to store fresh names, and to compare incoming names with previously stored ones. These finite machines extend Kaminski and Francez’s FiniteMemory Automata by being able to recognise globally fresh inputs, that is, names fresh in the whole current run. We examine the expressivity of FRA’s both from the aspect of accepted languages and of bisimulation equivalence. We establish primary properties and connections between automata of this kind, and answer key decidability questions. As a demonstrating example, we express the theory of the picalculus in FRA’s and characterise bisimulation equivalence by an appropriate, and decidable in the finitary case, notion in these automata.
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 ..."
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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
Full Abstraction for Nominal Scott Domains
, 2013
"... We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbitfinite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely m ..."
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We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbitfinite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojańczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and ‘definite description ’ over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallelor, to a programming language for recursively defined higherorder functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin’s classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higherorder functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.
Completeness and Incompleteness in Nominal Kleene Algebra
, 2014
"... Gabbay and Ciancia (2011) presented a nominal extension of Kleene algebra as a framework for trace semantics with dynamic allocation of resources, along with a semantics consisting of nominal languages. They also provided an axiomatization that captures the behavior of the scoping operator and its ..."
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Gabbay and Ciancia (2011) presented a nominal extension of Kleene algebra as a framework for trace semantics with dynamic allocation of resources, along with a semantics consisting of nominal languages. They also provided an axiomatization that captures the behavior of the scoping operator and its interaction with the Kleene algebra operators and proved soundness over nominal languages. In this paper we show that the axioms are complete and describe the free language models. 1
Specifying and Verifying Properties of Space
, 2014
"... The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems distributed in physical space. Traditional verification tec ..."
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The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems distributed in physical space. Traditional verification techniques are well suited to analyse the temporal evolution of programs; properties of space are typically not explicitly taken into account. We propose a methodology to verify properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to a more general setting, also encompassing discrete, graphbased structures. We further extend the framework with a spatial until operator, and define an efficient model checking procedure, implemented in a proofofconcept tool.
Denotational Semantics with Nominal Scott Domains
, 2014
"... When defining computations over syntax as data, one often runs into tedious issues concerning αequivalence and semantically correct manipulations of binding constructs. Here we study a semantic framework in which these issues can be dealt with automatically by the programming language. We take the ..."
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When defining computations over syntax as data, one often runs into tedious issues concerning αequivalence and semantically correct manipulations of binding constructs. Here we study a semantic framework in which these issues can be dealt with automatically by the programming language. We take the userfriendly ‘nominal’ approach in which bound objects are named. In particular, we develop a version of Scott domains within nominal sets and define two programming languages whose denotational semantics are based on those domains. The first language, λνPCF, is an extension of Plotkin’s PCF with names that can be swapped, tested for equality and locally scoped; although simple, it already exposes most of the semantic subtleties of our approach. The second language, PNA, extends the first with name abstraction and concretion so that it can be used for metaprogramming over syntax with binders. For both languages, we prove a full abstraction result for nominal Scott domains analogous to Plotkin’s classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for languages combining higherorder functions with some form of locally scoped names which uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.
www.gabbay.org.uk
"... We present a model of games based on nominal sequences, which generalise sequences with atoms and a new notion of coabstraction. This gives a new, precise, and compositional mathematical treatment of justification pointers in game semantics. Keywords: Game semantics, nominal sets, nominal abstractio ..."
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We present a model of games based on nominal sequences, which generalise sequences with atoms and a new notion of coabstraction. This gives a new, precise, and compositional mathematical treatment of justification pointers in game semantics. Keywords: Game semantics, nominal sets, nominal abstraction and coabstraction, equivariance
Semantics
"... out of context: nominal absolute denotations for firstorder logic and computation ..."
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out of context: nominal absolute denotations for firstorder logic and computation