## Imprecise and Approximate ComputationReal-time systems are now used in a wide variety of applications. Conventionally, they were configured at design to perform a given set of tasks and could not readily adapt to dynamic situations. The concept of imprecise and approximate computation has emerged as a promising approach to providing scheduling flexibility and enhanced dependability in dynamic real-time systems. The concept can be utilized in a wide variety of applications, including signal processing, machine vision, databases, networking, etc. For those who wish to build dynamic real-time systems which must deal safely with resource unavailability while continuing to operate, leading to situations where computations may not be carried through to completion, the techniques of imprecise and approximate computation facilitate the generation of partial results that may enable the system to operate safely and avert catastrophe. Audience: Of special interest to researchers. May be used as a supplementary text in courses on real-time systems. |

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### Contents

Chapter | 1 |

_ System Structure ODOb0O 2 Stages of Task Existence Within the System | 4 |

Example of Imprecise Computation Prediction for N | 8 |

NGp Algorithm 5 NGM Algorithm 6 NG1 Algorithm | 9 |

NGH Algorithm | 10 |

General Transitional Notice Generator | 11 |

NGM to NGp Switching Algorithm | 12 |

NG1 to NGp Switching Algorithm 14 NGH to NGP Switching Algorithm 15 Mean Waiting Time | 13 |

APPROXIMATE REASONING USING | 43 |

Chapter 4 | 44 |

Chapter 5 | 58 |

Chapter 2 | 60 |

INTEGRATING UNBOUNDED SOFTWARE | 63 |

An example relationship between 1 r and T | 70 |

REPLICATED IMPRECISE COMPUTATIONS | 87 |

Chapter 6 | 88 |

Mean Computation Time | 14 |

Mean Time Without Notice | 19 |

Chapter 7 | 22 |

REPRESENTING AND SCHEDULING | 23 |

Chapter 2 | 24 |

Two examples of iterative reﬁnement task groups The solid lines indicate a tasksubtask relationship The dashed lines indicate a precedence constraint | 27 |

An example of a multiple method task group The solid lines indicate tasksubtask relationships | 28 |

A SURVEY OF SCHEDULING RESULTS | 35 |

Chapter 3 | 36 |

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Allocate algorithm anytime algorithms approach approximate answer approximate object approximate relation approximation algorithm Artiﬁcial Intelligence assigned assume cartesian product clone allocation compilation complete components Computer Science Conference on Artiﬁcial conﬂicts constraints data objects database deadline deﬁned denote design-to-time epilogue task exact answer example execution expected utility feasible task allocations Figure ﬁnd ﬁrst greedy algorithm hard workload IEEE imprecise computation input intermediate results interruptible iterative reﬁnement J. W. S. Liu load mandatory maximum processor utilization minimizing Modify algorithm monitoring monotonically multiprocessors node non-faulty PE’s NP-hard number of clones number of tasks operation optimal optional task PDSA performance proﬁles periodic tasks precise notices priority Proceedings produce queue real-time computing reconﬁguration relational algebra repair server resource requirements run-time satisﬁcing schedulability threshold scheduling algorithm Section sieve functions single processor solution subtasks Systems Symposium task allocation task computation task structures task system techniques tuples update upper bound weighted error