## Limits to Parallel Computation: P-Completeness TheoryThis book provides a comprehensive analysis of the most important topics in parallel computation. It is written so that it may be used as a self-study guide to the field, and researchers in parallel computing will find it a useful reference for many years to come. The first half of the book consists of an introduction to many fundamental issues in parallel computing. The second half provides lists of P-complete- and open problems. These lists will have lasting value to researchers in both industry and academia. The lists of problems, with their corresponding remarks, the thorough index, and the hundreds of references add to the exceptional value of this resource. While the exciting field of parallel computation continues to expand rapidly, this book serves as a guide to research done through 1994 and also describes the fundamental concepts that new workers will need to know in coming years. It is intended for anyone interested in parallel computing, including senior level undergraduate students, graduate students, faculty, and people in industry. As an essential reference, the book will be needed in all academic libraries. |

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### Contents

3 | |

IV | 8 |

VI | 11 |

VII | 13 |

VIII | 16 |

IX | 17 |

X | 19 |

XI | 21 |

XLI | 103 |

XLII | 108 |

XLIII | 109 |

XLIV | 111 |

XLV | 114 |

XLVI | 117 |

XLVII | 119 |

XLVIII | 121 |

XII | 26 |

XIII | 30 |

XIV | 33 |

XV | 38 |

XVI | 41 |

XVII | 44 |

XVIII | 45 |

XIX | 46 |

XXI | 47 |

XXII | 49 |

XXIII | 52 |

XXIV | 54 |

XXVI | 57 |

XXVII | 59 |

XXVIII | 61 |

XXIX | 62 |

XXX | 63 |

XXXI | 68 |

XXXII | 69 |

XXXIII | 71 |

XXXIV | 75 |

XXXV | 87 |

XXXVI | 90 |

XXXVII | 94 |

XXXVIII | 96 |

XXXIX | 98 |

XL | 100 |

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### Common terms and phrases

acyclic binary bits Boolean circuit bounded circuit family Circuit Value Problem complexity class Computer Science constructed context-free decision problem defined Definition denote depth-first search designated deterministic edge encoding example fanin fanout feasible highly parallel function gadget Given Goldschlager graph G greedy algorithm Greenlaw Hint induced subgraph inherently sequential input instance integer Journal on Computing Karp labeled language layer Lemma lexicographically first maximal logarithmic space many-one maximal independent set maximum flow Mayr memory cells Monotone Circuit Value NC algorithm number of processors O(logn optimal oracle output gate P-complete P-complete problems parallel algorithm parallel complexity parallel computation pebble planar polylogarithmic polynomial PRAM prob problem is P-complete proof reduction Reference remains P-complete Remarks restricted Ruzzo search problem segment sequential algorithm shared memory simulation solved speedup string Symposium Theorem theory topological order tree Turing machine Turing reducibility unary undirected graph variant vertex vertices