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26
Causality Interfaces and Compositional Causality Analysis
 FIT 2005 PRELIMINARY VERSION
, 2005
"... In this paper, we consider concurrent models of computation where ”actors” (components that are in charge of their own actions) communicate by exchanging messages. The interfaces of actors principally consist of “ports,” which mediate the exchange of messages. Actororiented architectures contrast w ..."
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Cited by 13 (10 self)
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In this paper, we consider concurrent models of computation where ”actors” (components that are in charge of their own actions) communicate by exchanging messages. The interfaces of actors principally consist of “ports,” which mediate the exchange of messages. Actororiented architectures contrast with and complement objectoriented models by emphasizing the exchange of data between concurrent components rather than transfer of control. Examples of such models of computation include the classical actor model, synchronous languages, dataflow models, and discreteevent models. Many of these models of computation benefit considerably from having access to causality information about the components. This paper augments the interfaces of such components to include such causality information. It shows how this causality information can be algebraically composed so that compositions of components acquire causality interfaces that are inferred from their components and the interconnections. We illustrate the use of these causality interfaces to statically analyze discreteevent models for uniqueness of behaviors, synchronous models for causality loops, and dataflow models for schedulability.
Behavioural Differential Equations and Coinduction for Binary Trees
"... Abstract. We study the set TA of infinite binary trees with nodes labelledinasemiringA from a coalgebraic perspective. We present coinductive definition and proof principles based on the fact that TA carries a final coalgebra structure. By viewing trees as formal power series, we develop a calculus ..."
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Cited by 5 (1 self)
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Abstract. We study the set TA of infinite binary trees with nodes labelledinasemiringA from a coalgebraic perspective. We present coinductive definition and proof principles based on the fact that TA carries a final coalgebra structure. By viewing trees as formal power series, we develop a calculus where definitions are presented as behavioural differential equations. We present a general format for these equations that guarantees the existence and uniqueness of solutions. Although technically not very difficult, the resulting framework has surprisingly nice applications, which is illustrated by various concrete examples. 1
A Coalgebraic Perspective on Linear Weighted Automata
, 2011
"... Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either ( ..."
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Cited by 4 (1 self)
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Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either (weighted) bisimilarity or (weighted) language equivalence. Coalgebras provide a categorical framework for the uniform study of statebased systems and their behaviours. In this work, we show that coalgebras can suitably model weighted automata in two different ways: coalgebras on
Observational Coalgebras and Complete Sets of Cooperations
, 2008
"... In this paper we introduce the notion of an observational coalgebra structure and of a complete set of cooperations. We demonstrate in various example the usefulness of these notions, in particular, we show how they give rise to coalgebraic proof and definition principles. ..."
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Cited by 3 (0 self)
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In this paper we introduce the notion of an observational coalgebra structure and of a complete set of cooperations. We demonstrate in various example the usefulness of these notions, in particular, we show how they give rise to coalgebraic proof and definition principles.
Sampling, Splitting and Merging in Coinductive Stream Calculus
"... Abstract. We study various operations for partitioning, projecting and merging streams of data. These operations are motivated by their use in dataflow programming and the stream processing languages. We use the framework of stream calculus and stream circuits for defining and proving properties of ..."
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Cited by 2 (2 self)
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Abstract. We study various operations for partitioning, projecting and merging streams of data. These operations are motivated by their use in dataflow programming and the stream processing languages. We use the framework of stream calculus and stream circuits for defining and proving properties of such operations using behavioural differential equations and coinduction proof principles. We study the invariance of certain well patterned classes of streams, namely rational and algebraic streams, under splitting and merging. Finally we show that stream circuits extended with gates for dyadic split and merge are expressive enough to realise some nonrational algebraic streams, thereby going beyond ordinary stream circuits.
On The Final Coalgebra Of Automatic Sequences
, 2011
"... Abstract. Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer s ..."
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Cited by 1 (1 self)
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Abstract. Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer science; and they appear in mathematics in many different ways, for instance in number theory. Examples of automatic sequences include the celebrated ThueMorse sequence and the RudinShapiro sequence. In this paper, we apply the coalgebraic perspective on streams to automatic sequences. We show that the set of automatic sequences carries a final coalgebra structure, consisting of the operations of head, even, and odd. This will allow us to show that automatic sequences are to (general) streams what rational languages are to (arbitrary) languages. 1