## 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

### Citations

3636 | Communicating sequential processes
- Hoare
- 1978
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- 1989
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- 1976
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- 1977
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Citation Context ...n compute arbitrary continuous input/output functions, angelic merge, and infinity-fair merge (which requires countably indeterminate branching), but that no such network can implement fair merge. In =-=[22]-=- the question of expressing fair merge is settled negatively essentially using the ideas suggested above. The fact that there is some sort of nonmonotonicity associated with fair merge (and amb) has b... |

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Citation Context ...a single sequence, in such a way that the output sequence produced in any complete computation is always a fair shuffle of the two input sequences. The angelic merge and infinity-fair merge processes =-=[23]-=- perform a function similar to that of the fair merge, but do not necessarily transmit all values that arrive on both inputs. Instead, they both satisfy the basic requirement that the output sequence ... |

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2 |
Private communication
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1 |
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1 |
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1 |
Cubri'c and P.Panangaden. Monotone and nonmonotone dataflow networks
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- 1993
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Citation Context ...ace sets and also introduced the dual concept, upper monotonicity. One can ask whether monotone automata compute exactly the lower monotone trace sets. In fact recent results of Cubric and Panangaden =-=[29]-=- show that there are lower monotone trace sets that cannot be implemented by any monotone automaton. The example is a simple, a fair stack. One can also show that fair stack cannot implement angelic m... |

1 |
On expressing fair merge with arnb
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- 1984
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Citation Context ...considered here, it is known that with McCarthy's arab primitive [10] one can produce countable branching and also angelic merge, but it has not been shown that one can program a fair merge with arnb =-=[1]-=-. In this paper, we show that countable indeterminacy alone is not sufficient for fairness; it is also necessary to branch based on the availability of input data. More precisely, we show that network... |

1 |
Rdductions Correctes et OptimaIes dans le Lambda CalcuI
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Citation Context ...s in a suitable sense is the input/output relation of a network of monotone port automata. Residuals have been used previously in the investigation of optimal reduction strategies for the ),-calculus =-=[6,19]-=- and term-rewriting systems [7,14]. In that work, residuals are used to keep track of what happens to one redex in a term while others are contracted. Our use is entirely analogous--a residual operati... |

1 |
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- 1982
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Citation Context ...a single sequence, in such a way that the output sequence produced in any complete computation is always a fair shuflte of the two input sequences. The angelic merge and infinity-fair merge processes =-=[23]-=- perform a function similar to that of the fair merge, but do not necessarily transmit all values that arrive on both inputs. Instead, they both satisfy the basic requirement that the output sequence ... |