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Computations, residuals, and the power of indeterminacy

  • Prakash Panangaden
  • Eugene W. Stark
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)

Abstract

We investigate the power of Kahn-style dataflow networks, with processes that may exhibit indeterminate behavior. Our main result is a theorem about networks of “monotone” processes, which shows: (1) that the input/output relation of such a network is a total and monotone relation; and (2) every relation that is total, monotone, and continuous in a certain sense, is the input/output relation of such a network. Now, the class of monotone networks includes networks that compute arbitrary continuous input/output functions, an “angelic merge” network, and an “infinity-fair merge” network that exhibits countably indeterminate branching. Since the “fair merge” relation is neither monotone nor continuous, a corollary of our main result is the impossibility of implementing fair merge in terms of continuous functions, angelic merge, and infinity-fair merge.

Our results are established by applying the powerful technique of “residuals” to the computations of a network. Residuals, which have previously been used to investigate optimal reduction strategies for the λ-calculus, have recently been demonstrated by one of the authors (Stark) also to be of use in reasoning about concurrent systems. Here, we define the general notion of a “residual operation” on an automaton, and show how residual operations defined on the components of a network induce a certain preorder ⫇ on the set of computations of the network. For networks of “monotone port automata,” we show that the “fair” computations coincide with ⫇-maximal computations. Our results follow from this extremely convenient property.

Keywords

Input Transition Output Transition Input Buffer Recursive Program Input History 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Prakash Panangaden
    • 1
  • Eugene W. Stark
    • 2
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA
  2. 2.Department of Computer ScienceState University of New York at Stony BrookStony BrookUSA

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