. This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding Multi-Agent 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 polynomial-like 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....

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 dataflow 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 a...

. This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding Multi-Agent 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...

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 (1996--1997) at Unit...

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

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 built-in 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 data-flow graph theory, and have to accommodate also relational aspects. Using functorial semantics into a Kleene category of “hyper-paths”, we formally capture the data-flow-with-choice aspects of this language and its implementation, providing also the framework for the necessary correctness proofs. 1

The paper presents a simple format for typed logics with states by adding a function for register update to standard typed lambda calculus. It is shown that universal validity of equality for this extended language is decidable (extending a well-known result of Friedman for typed lambda calculus) . This system is next extended to a full fledged typed dynamic logic, and it is illustrated how the resulting format allows for very simple and intuitive representations of dynamic semantics for natural language and denotational semantics for imperative programming. The proposal is compared with some alternative approaches to formulating typed versions of dynamic logics. Keywords: type theory, compositionality, denotational semantics, dynamic semantics 1 Introduction A slight extension to the format of typed lambda calculus is enough to model states (assignments of values to storage cells) in a very natural way. Let a set R of registers or storage cells be given. If we assume that the values...

Network algebra is proposed as a uniform algebraic framework for the description and analysis of dataflow networks. An equational theory, 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 synchronous and asynchronous dataflow networks, additional constants and axioms for connections are given; and corresponding process algebra models are introduced. The main difference between these models is in the interpretation of the identity connections, called wires in dataflow networks. The process algebra model for the asynchronous case is compared with previous models. Keywords & Phrases: dataflow networks, network algebra, process algebra, asynchronous dataflow, synchronous 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. y The first author has been partially supported by ESPRIT...

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 two-way 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...

Network algebra (NA) is proposed as a uniform algebraic framework for the description (and analysis) of dataflow 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 dataflow 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 dataflow networks: synchronous dataflow networks, asynchronous dataflow networks and fully asynchronous dataflow networks, respectively. For each case...