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16
The algebra of stream processing functions
, 1996
"... Dataflow networks are a model of concurrent computation. They consist of a collection of concurrent asynchronous processes which communicate by sending data over FIFO channels. In this paper we study the algebraic structure of the data ow networks and base their semantics on stream processing funct ..."
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Dataflow networks are a model of concurrent computation. They consist of a collection of concurrent asynchronous processes which communicate by sending data over FIFO channels. In this paper we study the algebraic structure of the data ow networks and base their semantics on stream processing functions. The algebraic theory is provided by the calculus of flownomials which gives a unified presentation of regular algebra and iteration theories. The kernel of the calculus is an equational axiomatization called Basic Network Algebra (BNA) for flowgraphs modulo graph isomorphism. We show that the algebra of stream processing functions called SPF (used for deterministic networks) and the algebra of sets of stream processing functions called PSPF (used for nondeterministic networks) are BNA algebras. As a byproduct this shows that both semantic models are compositional. We also identify the additional axioms satisfied by the branching components that correspond to constants in these two algebraic theories. For the deterministic case we study in addition the coarser equivalence relation on networks given by the inputoutput behaviour and provide a correct and complete axiomatization.
Reaction and Control I. Mixing Additive and Multiplicative Network Algebras
 Logic Journal of the IGPL
, 1996
"... . This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomi ..."
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. This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomials. It is a polynomiallike calculus for representing flowgraphs and their behaviours. An `additive' interpretation of the calculus was intensively developed to study control flowcharts and finite automata. For instance, regular algebra and iteration theories are included in a unified presentation. On the other hand, a `multiplicative' interpretation of the calculus of flownomials was developed to study dataflow networks. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras will contribute to the understanding of distributed computation. The role of this first paper is to present a few motivating examples. To appear in Journal of IGPL....
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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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
A short tour on FEST
 Preprint Series in Mathematics, Institute of Mathematics, Romanian Academy, No. 38/December
, 1996
"... . This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. The claim of this series of papers is that ..."
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Cited by 4 (0 self)
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. This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras (MixNA) will contribute to the understanding of distributed computation. The aim of this part of the series is to make a short introduction to the kernel language FEST (Flownomial Expressions and System Tasks) based on MixNA. 1 Introduction FEST (Flownomial Expressions and System Tasks) is a kernel language under construction at UniBuc. Its main feature is a full integration of reactive and control modules. It has a clear mathematical semantics based on MixNA. 2 Unstructured FEST programs The unstructured FEST programs freely combine control and reactive modules. The wording "unstructured" referees to the fact that the basic s...
Axiomatizing Mixed Relations
, 1997
"... This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. The claim of this series of papers is that the ..."
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Cited by 4 (0 self)
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This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras (MixNA) will contribute to the understanding of distributed computation. A study of the classes of finite relations as enriched strict monoidal categories is presented in [CaS91]. The relations there are interpreted as connections in flowchart schemes, hence an "angelic" theory of relations is used. Finite relations may be used to model the connections between the components of dataflow networks [BeS95, BrS96], as well. The corresponding algebras are slightly different enriched strict monoidal categories modelling a "forwarddemonic" theory of relations. In order to obtain a full model for parallel programs one needs to mix control...
Network Algebra for Asynchronous Dataflow
, 1997
"... Network algebra is proposed as a uniform algebraic framework for the description and analysis of dataflow networks. An equational theory of networks, called BNA (Basic Network Algebra), is presented. BNA, which is essentially a part of the algebra of flownomials, captures the basic algebraic prop ..."
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Network algebra is proposed as a uniform algebraic framework for the description and analysis of dataflow networks. An equational theory of networks, called BNA (Basic Network Algebra), is presented. BNA, which is essentially a part of the algebra of flownomials, captures the basic algebraic properties of networks. For asynchronous dataflow networks, additional constants and axioms are given; and a corresponding process algebra model is introduced. This process algebra model is compared with previous models for asynchronous dataflow. Keywords & Phrases: dataflow networks, network algebra, process algebra, asynchronous dataflow, feedback, merge anomaly, history models, oracle based models, trace models. 1994 CR Categories: F.1.1, F.1.2, F.3.2., D.1.3., D.3.1. This paper is an abridged version of [1]. The full version covers synchronous dataflow networks as well. y Partially supported by ESPRIT BRA 8533 (NADA) and ESPRIT BRA 6454 (CONFER). x On leave (19961997) at Unit...
A Complete Proof System for Nested Term Graphs
 In Proc. HOA '95
, 1995
"... Nested Term Graphs are syntactic representations of cyclic term graphs. Via a simple translation they contain terms as a subset. There exists a characterization of the terms that unwind to the same tree, presented as a complete proof system. This paper gives a similar characterization for Nested T ..."
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Nested Term Graphs are syntactic representations of cyclic term graphs. Via a simple translation they contain terms as a subset. There exists a characterization of the terms that unwind to the same tree, presented as a complete proof system. This paper gives a similar characterization for Nested Term Graphs. The semantics of tree unwinding is presented via bisimulations. 1
Network Algebra with Demonic Relation Operators
"... Relations with demonic operators are used in studies related to predicate transformer semantics of nondeterministic programs, to model the connection wires in synchronous dataflow networks, or in process algebra setting to model the communication between agents and their envirnoments. The aim of thi ..."
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Relations with demonic operators are used in studies related to predicate transformer semantics of nondeterministic programs, to model the connection wires in synchronous dataflow networks, or in process algebra setting to model the communication between agents and their envirnoments. The aim of this paper is to provide equational axiomatisations for various classes of finite relations with demonic (including looping) operators. We present axiomatisations for three types of demonic calculi: i.e. calculi for relations with forward demonic , backward demonic  or twoway demonic operators. The algebraic structures involved are basic network algebras (a certain class of symmetric strict monoidal categories enriched with a looping operation  feedback) with appropriate ramification and identification constants. Keywords & Phrases: network algebra, relations, demonic calculus, synchronous dataflow networks, feedback. The second author has been partially supported by the HCM Cooperati...
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"... We use Tarski's relational calculus to construct a model of linear temporal logic. Both discrete and dense time are covered and we obtain denotational domains for a large variety of reactive systems. Keywords : Relational algebra, reactive systems, temporal algebra, temporal logic. 1 ..."
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We use Tarski's relational calculus to construct a model of linear temporal logic. Both discrete and dense time are covered and we obtain denotational domains for a large variety of reactive systems. Keywords : Relational algebra, reactive systems, temporal algebra, temporal logic. 1
Network Algebra for Synchronous and Asynchronous Dataflow
"... Network algebra (NA) is proposed as a uniform algebraic framework for the description (and analysis) of data ow networks. The core of this algebraic setting is provided by an equational theory called Basic Network Algebra (BNA). It constitutes a selection of primitives and identities from the algebr ..."
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Network algebra (NA) is proposed as a uniform algebraic framework for the description (and analysis) of data ow networks. The core of this algebraic setting is provided by an equational theory called Basic Network Algebra (BNA). It constitutes a selection of primitives and identities from the algebra of flownomials due to [Ste86] and [CaS88&89]. Both synchronous and asynchronous data ow networks are then investigated from the viewpoint of network algebra. To this end the NA primitives are defined such that the identities of BNA hold. These axioms are particularly strict about the role of the connections, which will be called flows of data. We describe three interpretations of the connections that satisfy the BNA identities: minimal stream delayers, stream delayers and stream retimers. Each of the above possibilities leads to a class of data ow networks: synchronous data ow networks, asynchronous data ow networks and fully asynchronous data ow networks, respectively. For each case stream transformer and process algebra models are introduced and compared.