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International Colloquium on Automata, Languages, and Programming

ICALP 1988: Automata, Languages and Programming pp 439–454Cite as

Computations, residuals, and the power of indeterminacy

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Part of the book series: Lecture Notes in Computer Science ((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.

Research supported in part by NSF Grant DCR-8602072.

Research supported in part by NSF Grant CCR-8702247.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Cornell University, 14853, Ithaca, NY, USA

    Prakash Panangaden

  2. Department of Computer Science, State University of New York at Stony Brook, 11794, Stony Brook, NY, USA

    Eugene W. Stark

Authors
  1. Prakash Panangaden
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  2. Eugene W. Stark
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Timo Lepistö Arto Salomaa

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© 1988 Springer-Verlag Berlin Heidelberg

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Panangaden, P., Stark, E.W. (1988). Computations, residuals, and the power of indeterminacy. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_133

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  • DOI: https://doi.org/10.1007/3-540-19488-6_133

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19488-0

  • Online ISBN: 978-3-540-39291-0

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