## Computations, residuals and the power of indeterminacy (1988)

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Venue: | In Timo Lepisto and Arto Salomaa, editors, Proceedings of the Fifteenth ICALP |

Citations: | 20 - 10 self |

### BibTeX

@INPROCEEDINGS{Panangaden88computations,residuals,

author = {Prakash Panangaden and Eugene W. Stark T},

title = {Computations, residuals and the power of indeterminacy},

booktitle = {In Timo Lepisto and Arto Salomaa, editors, Proceedings of the Fifteenth ICALP},

year = {1988},

pages = {439--454},

publisher = {Springer-Verlag}

}

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### Abstract

We investigate the power of Katm-style datattow 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 inpu*~/output functions, an "angelic merge " network, and an "ilffinity-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 powerftll technique of "residuals " to the computations of a network. Residuals, which have previously been used to investigate optimal reduction strategies for the A-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 E on the set of computations of the network. For networks of "monotone port automata, " we show that the "fair " computations coincide with X-maximal computations. Our results follow from this extremely convenient property. 1