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14
Geometry of Interaction and Linear Combinatory Algebras
, 2000
"... this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by S ..."
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Cited by 44 (10 self)
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this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by Stefanescu (Stefanescu 2000).) However, the first author realized, following a stimulating discussion with Gordon Plotkin, that traced monoidal categories provided a common denominator for the axiomatics of both the Girardstyle and AbramskyJagadeesanstyle versions of the Geometry of Interaction, at the basic level of the multiplicatives. This insight was presented in (Abramsky 1996), in which Girardstyle GoI was dubbed "particlestyle", since it concerns information particles or tokens flowing around a network, while the AbramskyJagadeesan style GoI was dubbed "wavestyle", since it concerns the evolution of a global information state or "wave". Formally, this distinction is based on whether the tensor product (i.e. the symmetric monoidal structure) in the underlying category is interpreted as a coproduct (particle style) or as a product (wave style). This computational distinction between coproduct and product interpretations of the same underlying network geometry turned out to have been partially anticipated, in a rather di#erent context, in a pioneering paper by E. S. Bainbridge (Bainbridge 1976), as observed by Dusko Pavlovic. These two forms of interpretation, and ways of combining them, have also been studied recently in (Stefanescu 2000). He uses the terminology "additive" for coproductbased (i.e. our "particlestyle") and "multiplicative" for productbased (i.e. our "wavestyle"); this is not suitable for our purposes, because of the clash with Linear Logic term...
Some Algebraic Laws for Spans (and Their Connections With MultiRelations)
 Proceedings of RelMiS 2001, Workshop on Relational Methods in Software. Electronic Notes in Theoretical Computer Science, n.44 v.3, Elsevier Science (2001
, 2001
"... This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets. O ..."
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Cited by 9 (3 self)
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This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets. Our results nd analogous counterparts in (and are partly inspired by) the theory of relational algebras, thus our paper also shed some light on the relationship between (co)spans and the categories of (multi)relations and of equivalence relations. And, since (co)spans yields an intuitive presentation in terms of dynamical system with input and output interfaces, our results introduce an expressive, twofold algebra that can serve as a specication formalism for rewriting systems and for composing software modules and open programs. Key words: Spans, multirelations, monoidal categories, system specications. Introduction The use of spans [1,6] (and of the dual notion of cospans) have been...
Connector Colouring I: Synchronisation and Context Dependency
, 2006
"... Reo is a coordination model based on circuitlike connectors which coordinate components through the interplay of data flow, synchronisation and mutual exclusion, state, and contextdependent behaviour. This paper proposes a scheme based on connector colouring for determining the behaviour of a Reo ..."
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Cited by 7 (2 self)
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Reo is a coordination model based on circuitlike connectors which coordinate components through the interplay of data flow, synchronisation and mutual exclusion, state, and contextdependent behaviour. This paper proposes a scheme based on connector colouring for determining the behaviour of a Reo connector by resolving its context dependent synchronisation and mutual exclusion constraints. Colouring a Reo connector in a specific state with given boundary conditions (I/O requests) provides a means to determine the routing alternatives for data flow. Our scheme has the advantage over previous models in that it is simpler to implement and that it models Reo connectors more closely to their envisaged semantics than existing formal models.
Finite dimensional vector spaces are complete for traced symmetric monoidal categories
 in: Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday, Lecture Notes in Computer Science 4800 (2008
"... Abstract. We show that the category FinVectk of finite dimensional vector spaces and linear maps over any field k is (collectively) complete for the traced symmetric monoidal category freely generated from a signature, provided that the field has characteristic 0; this means that for any two differe ..."
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Cited by 7 (0 self)
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Abstract. We show that the category FinVectk of finite dimensional vector spaces and linear maps over any field k is (collectively) complete for the traced symmetric monoidal category freely generated from a signature, provided that the field has characteristic 0; this means that for any two different arrows in the free traced category there always exists astrongtracedfunctorintoFinVectk which distinguishes them. Therefore two arrows in the free traced category are the same if and only if they agree for all interpretations in FinVectk. 1
Controlflow semantics for assemblylevel dataflow graphs
 8th Intl. Seminar on Relational Methods in Computer Science, RelMiCS 2005, volume 3929 of LNCS
, 2006
"... Abstract. As part of a larger project, we have built a declarative assembly language that enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. Since the key design poi ..."
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Cited by 5 (2 self)
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Abstract. As part of a larger project, we have built a declarative assembly language that enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. Since the key design points for this language are to only describe data flow, have builtin facilities for redundancies, and still have code that looks like assembler, by virtue of consisting mainly of assembly instructions, we are basing the theoretical foundations on dataflow graph theory, and have to accommodate also relational aspects. Using functorial semantics into a Kleene category of “hyperpaths”, we formally capture the dataflowwithchoice aspects of this language and its implementation, providing also the framework for the necessary correctness proofs. 1
Algebra of Networks  Modeling simple networks, as well as complex interactive systems
 In: Proof and SystemReliability, Proc. Marktoberdorf Summer School 2001, Kluwer (2002), 4978. A., Sofronia A., Stefanescu G.: Highlevel Structured Interactive
"... The rst part of the paper contains an overview of Network Algebra (NA) book [35]. The second part introduces nite interactive systems as an abstract mathematical model of agents' behaviour and their interaction. ..."
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Cited by 2 (2 self)
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The rst part of the paper contains an overview of Network Algebra (NA) book [35]. The second part introduces nite interactive systems as an abstract mathematical model of agents' behaviour and their interaction.
Highlevel Structured Interactive Programs with Registers and Voices 1,2
"... Abstract: A model (consisting of rvsystems), a core programming language (for developing rvprograms), several specification and analysis techniques appropriate for modeling, programming and reasoning about interactive computing systems have been introduced by Stefanescu in 2004 using register mach ..."
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Cited by 2 (1 self)
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Abstract: A model (consisting of rvsystems), a core programming language (for developing rvprograms), several specification and analysis techniques appropriate for modeling, programming and reasoning about interactive computing systems have been introduced by Stefanescu in 2004 using register machines and spacetime duality, see [Stefanescu 2006, Stefanescu 2006b]. Later on, Dragoi and Stefanescu have introduced structured programming techniques for programming rvsystems and have presented a kernel programming language AGAPIA v0.1 for interactive computing systems, see [Dragoi and Stefanescu 2006a, Dragoi and Stefanescu 2006b]. AGAPIA v0.1 has a restricted format for program construction, using a “3level ” grammar for their definition: the procedure starts with simple while programs, then modules are defined, and finally AGAPIA v0.1 programs are obtained applying structured rvprogramming statements on top of modules. In the current paper the above restriction is completely removed. By an appropriate reshaping interface technique, general programs may be encapsulated into modules, allowing to reiterate the above “3level ” construction of programs, now starting with arbitrary AGAPIA programs, not with simple while programs. This way, highlevel interactive programs are obtained. The extended version is called AGAPIA v0.2. As a case study we consider a cluster of computers, each having a dynamic set of running processes. We present a protocol for the communication and termination detection in this system and implement the protocol in our AGAPIA v0.2 language. We also describe the operational semantics of the program using highlevel scenarios, i.e., scenarios where, recursively, the cells may themselves contain scenarios, at a lower, refined level.
"Interactive systems"  from a natural language expression, to a mathematical concept
"... This paper gives a brief introduction to interactive systems, an abstract mathematical model of agents' behavior and their interaction. The paper contains the denition of interactive systems, examples, a few simple properties and a comparison with some other similar models. 1 ..."
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Cited by 1 (0 self)
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This paper gives a brief introduction to interactive systems, an abstract mathematical model of agents' behavior and their interaction. The paper contains the denition of interactive systems, examples, a few simple properties and a comparison with some other similar models. 1
Synthesising and Verifying MultiCore Parallelism in Categories of Nested Code Graphs
, 2008
"... We present the MultiCore layer of the larger Coconut project to support highperformance, highassurance scientific computation. Programs are represented by nested code graphs, using domain specific languages. At the MultiCore level, the language is very restricted, in order to restrict control fl ..."
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We present the MultiCore layer of the larger Coconut project to support highperformance, highassurance scientific computation. Programs are represented by nested code graphs, using domain specific languages. At the MultiCore level, the language is very restricted, in order to restrict control flow to nonbranching, synchronising control flow, which allows us to treat multicore parallelism in essentially the same way as instructionlevel parallelism for pipelined multiissue processors. The resulting schedule is then presented as a “locally sequential program”, which, like highquality conventional assembly code in the singlecore case, is arranged for hiding latencies at execution time so that peak performance can be reached, and can also be understood by programmers. We present an efficient, incremental algorithm capable of verifying the soundness of the communication aspects of such programs.
A quantum double construction in Rel
, 2010
"... We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of ..."
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We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of