Ebook: Structural Complexity I

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.

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This is the first volume of a systematic two-volume presentation of the various areas of research on structural complexity. The theory of algorithmic complexity, a part of the mathematical theory of computation, can be approached from several points of view, one of which is the structural one.
This volume is written for undergraduate students who have taken a first course in Formal Language Theory. It presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory.
The second corrected edition has been extended by an appendix with recent results on nondeterministic space classes and updated with regard to the bibliographical remarks and the references.

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This is the first volume of a systematic two-volume presentation of the various areas of research on structural complexity. The theory of algorithmic complexity, a part of the mathematical theory of computation, can be approached from several points of view, one of which is the structural one.
This volume is written for undergraduate students who have taken a first course in Formal Language Theory. It presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory.
The second corrected edition has been extended by an appendix with recent results on nondeterministic space classes and updated with regard to the bibliographical remarks and the references.
Content:
Front Matter....Pages I-XIII
Introduction....Pages 1-5
Basic Notions About Models of Computation....Pages 6-35
Time and Space Bounded Computations....Pages 36-58
Central Complexity Classes....Pages 59-86
Time Bounded Turing Reducibilities....Pages 87-103
Nonuniform Complexity....Pages 104-135
Probabilistic Algorithms....Pages 136-156
Uniform Diagonalization....Pages 157-167
The Polynomial Time Hierarchy....Pages 168-185
Back Matter....Pages 186-210

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This is the first volume of a systematic two-volume presentation of the various areas of research on structural complexity. The theory of algorithmic complexity, a part of the mathematical theory of computation, can be approached from several points of view, one of which is the structural one.
This volume is written for undergraduate students who have taken a first course in Formal Language Theory. It presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory.
The second corrected edition has been extended by an appendix with recent results on nondeterministic space classes and updated with regard to the bibliographical remarks and the references.
Content:
Front Matter....Pages I-XIII
Introduction....Pages 1-5
Basic Notions About Models of Computation....Pages 6-35
Time and Space Bounded Computations....Pages 36-58
Central Complexity Classes....Pages 59-86
Time Bounded Turing Reducibilities....Pages 87-103
Nonuniform Complexity....Pages 104-135
Probabilistic Algorithms....Pages 136-156
Uniform Diagonalization....Pages 157-167
The Polynomial Time Hierarchy....Pages 168-185
Back Matter....Pages 186-210
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