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**1 - 4**of**4**### Kahn Principle for Linear Dynamic Networks

, 1994

"... We consider dynamic Kahn-like data flow networks, i.e. networks consisting of deterministic processes each of which is able to expand into a subnetwork. The Kahn principle states that such networks are deterministic, i.e. that for each network we have that each execution provided with the same in ..."

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We consider dynamic Kahn-like data flow networks, i.e. networks consisting of deterministic processes each of which is able to expand into a subnetwork. The Kahn principle states that such networks are deterministic, i.e. that for each network we have that each execution provided with the same input delivers the same output. Moreover, the principle states that the output streams of such networks can be obtained as the smallest fixed point of a suitable operator derived from the network specification. This paper is meant as a first step towards a proof of this principle. For a specific subclass of dynamic networks, linear arrays of processes, we define a transition system yielding an operational semantics which defines the meaning of a net as the set of all possible interleaved executions. We then prove that, although on the execution level there is much nondeterminism, this nondeterminism disappears when viewing the system as a transformation from an input stream to an outpu...

### Kahn's Fixed-Point Characterization for Linear Dynamic Networks

, 1997

"... . We consider dynamic Kahn-like data#ow networks de#ned by a simple language L containing the fork-statement. The #rst part of the Kahn principle states that such networks are deterministic on the I#O level : for each network, di#erent executions provided with the same input deliver the same out ..."

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. We consider dynamic Kahn-like data#ow networks de#ned by a simple language L containing the fork-statement. The #rst part of the Kahn principle states that such networks are deterministic on the I#O level : for each network, di#erent executions provided with the same input deliver the same output. The second part of the principle states that the function from input streams to output streams #which is now de#ned because of the #rst part# can be obtained as a #xed point of a suitable operator derived from the network speci#cation. The #rst part has been proven by us in #BN96, BN97#. To prove the second part, we will use the metric framework. We introduce a nondeterministic transition system NT from whichwe derive an operational semantics On.We also de#ne a deterministic transition system DT and prove that the operational semantics Od derived from DT is the same as On . Finally, we de#ne a denotational semantics D and prove D = Od . This implies On = D. Thus the second par...