Structural Complexity I

Jose L. Balcazar

ISBN 10: 3642792375 / ISBN 13: 9783642792373

Editore: Springer Berlin Heidelberg, 2011

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Druck auf Anfrage Neuware - Printed after ordering - In the six years since the first edition of this book was published, the field of Structural Complexity has grown quite a bit. However, we are keeping this volume at the same basic level that it had in the first edition, and the only new result incorporated as an appendix is the closure under complementation of nondeterministic space classes, which in the previous edition was posed as an open problem. This result was already included in our Volume II, but we feel that due to the basic nature of the result, it belongs to this volume. There are of course other important results obtained during these last six years. However, as they belong to new areas opened in the field they are outside the scope of this fundamental volume. Other changes in this second edition are the update of some Bibliograph ical Remarks and references, correction of many mistakes and typos, and a renumbering of the definitions and results. Experience has shown us that this new numbering is a lot more friendly, and several readers have confirmed this opinion. For the sake of the reader of Volume II, where all references to Volume I follow the old numbering, we have included here a table indicating the new number corresponding to each of the old ones.

Codice articolo 9783642792373

Dati bibliografici

• Titolo: Structural Complexity I
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3642792375
• ISBN 13: 9783642792373
• Rilegatura: Taschenbuch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 13 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 13 millimetri di profondità
• Peso: 353 grammi

Descrizione articolo

Riassunto

This first of the two-volume presentation of structural complexity introduces the background necessary for the understanding of complexity theory. It is written for undergraduate students with basic knowledge in Formal Language Theory and contains about 140 exercises and many bibliographical remarks. This second, corrected edition includes an appendix with recent results and an update of the references.

Contenuti

1 Introduction.- 2 Basic Notions About Models of Computation.- 1.1 Introduction.- 1.2 Alphabets, Words, Sets, and Classes.- 1.3 Inclusion Modulo Finite Variants.- 1.4 Boolean Formulas.- 1.5 Models of Computation: Finite Automata.- 1.6 Models of Computation: Taring Machines.- 1.7 Models of Computation: Nondeterministic Turing Machines.- 1.8 Models of Computation: Oracle Turing Machines.- 1.9 Bibliographical Remarks.- 3 Time and Space Bounded Computations.- 2.1 Introduction.- 2.2 Orders of Magnitude.- 2.3 Running Time and Work Space of Turing Machines.- 2.4 Time and Space Constructibility.- 2.5 Bounding Resources: Basic Definitions and Relationships.- 2.6 Bibliographical Remarks.- 4 Central Complexity Classes.- 3.1 Introduction.- 3.2 Definitions, Properties, and Examples.- 3.3 Computing Functions: Invertibility and Honesty.- 3.4 Polynomial Time Many-one Reducibility.- 3.5 “Natural” NP-complete Sets.- 3.6 “Natural” PSPACE-complete Sets.- 3.7 Padding Arguments.- 3.8 Space Bounded Reducibility.- 3.9 Exercises.- 3.10 Bibliographical Remarks.- 5 Time Bounded Turing Reducibilities.- 4.1 Introduction.- 4.2 Polynomial Time Turing Reducibility: Relativized Classes.- 4.3 Tally and Sparse Sets in NP.- 4.4 Strong Nondeterministic Polynomial Time Reducibility.- 4.5 Self-Reducibility.- 4.6 Exercises.- 4.7 Bibliographical Remarks.- 6 Nonuniform Complexity.- 5.1 Introduction.- 5.2 Classes Defined by Advice Functions.- 5.3 Boolean Circuit Complexity.- 5.4 Turing Machines and Boolean Circuits.- 5.5 Polynomial Advice.- 5.6 Logarithmic Advice.- 5.7 Self-Producible Circuits.- 5.8 A Lower Bound to the Circuit Size of Boolean Functions.- 5.9 Other Nonuniform Complexity Measures.- 5.10 Exercises.- 5.11 Bibliographical Remarks.- 7 Probabilistic Algorithms.- 6.1 Introduction.- 6.2 The Probabilistic Computational Model.- 6.3 Polynomial Time Probabilistic Classes.- 6.4 Bounded Error Probability.- 6.5 Nonuniform Properties of BPP.- 6.6 Zero Error Probability.- 6.7 Exercises.- 6.8 Bibliographical Remarks.- 8 Uniform Diagonalization.- 7.1 Introduction.- 7.2 Presentability and Other Properties.- 7.3 The Main Theorem.- 7.4 Applications.- 7.5 Exercises.- 7.6 Bibliographical Remarks.- 9 The Polynomial Time Hierarchy.- 8.1 Introduction.- 8.2 Definition and Properties.- 8.3 Characterization and Consequences.- 8.4 Complete Sets and Presentability.- 8.5 BPP and the Polynomial Time Hierarchy.- 8.6 Exercises.- 8.7 Bibliographical Remarks.- References.- Appendix Complementation via Inductive Counting.- Author Index.- Symbol Index.