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A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 27 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...
A Simple Generalization of Kahn's Principle to Indeterminate Dataflow Networks
 Semantics for Concurrency, Leicester
, 1990
"... Kahn's principle states that if each process in a dataflow network computes a continuous input/output function, then so does the entire network. Moreover, in that case the function computed by the network is the least fixed point of a continuous functional determined by the structure of the network ..."
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Cited by 8 (2 self)
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Kahn's principle states that if each process in a dataflow network computes a continuous input/output function, then so does the entire network. Moreover, in that case the function computed by the network is the least fixed point of a continuous functional determined by the structure of the network and the functions computed by the individual processes. Previous attempts to generalize this principle in a straightforward way to "indeterminate" networks, in which processes need not compute functions, have been either too complex or have failed to give results consistent with operational semantics. In this paper, we give a simple, direct generalization of Kahn's fixedpoint principle to a large class of indeterminate dataflow networks, and we prove that results obtained by the generalized principle are in agreement with a natural operational semantics. 1 Introduction Dataflow networks are a parallel programming paradigm in which a collection of concurrently and asynchronously executing s...
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
Connectedness and Synchronization
 In Images of Programming. North Holland Publ. Co
, 1991
"... this paper we supplement the taxonomy list above with another kind of semantical domains, namely we consider connected relations. In the most general setting connected relations are parametrized by a given domain D which obeys some specific finiteness conditions; we say that D is an Fdomain [RT3]. ..."
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Cited by 3 (3 self)
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this paper we supplement the taxonomy list above with another kind of semantical domains, namely we consider connected relations. In the most general setting connected relations are parametrized by a given domain D which obeys some specific finiteness conditions; we say that D is an Fdomain [RT3]. In the particular case when D is the domain of natural numbers, connected relations appeared first in [Maz1] under the name of multitrees. For connected relations one can define a natural version of synchronization (strong conjunction).
Modularity and Expressibility for Nets of Relations
, 1996
"... Modularity reflects the Frege Principle: any two expressions expr 1 and expr 2 which have the same meaning (semantics) can be replaced by each other in every appropriate context C[ ] without changing the meaning of the overall expression. In [18] we identified observable relations and nets of obser ..."
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Cited by 2 (0 self)
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Modularity reflects the Frege Principle: any two expressions expr 1 and expr 2 which have the same meaning (semantics) can be replaced by each other in every appropriate context C[ ] without changing the meaning of the overall expression. In [18] we identified observable relations and nets of observable relations as appropriate tools for the investigation of dataflow networks over nondeterministic agents. The observable relations are the InputOutput behaviors of (in general nondeterministic) dataflow agents. Moreover, the semantics of nets of observable relations is consistent with the inputoutput behavior of dataflow agents. In [18, 19] we showed that the main source of the BrockAckerman anomaly [2] is in the semantics of nets of relations. But it turns out that this semantics is not modular. The central objective of this paper is the characterization of modular classes of relations and hence indirectly the set of dataflow nets without anomalies. Another major theme which plays a ...