Structural complexity
著者
書誌事項
Structural complexity
（EATCS monographs on theoretical computer science, v. 11,
Springer-Verlag, c1988-c1990
- v. 1 : gw
- v. 1 : us
- v. 2 : gw
- v. 2 : us
- v. 2 : [pbk]
大学図書館所蔵 件 / 全69件
-
:v. 1 : gw026211998000694,
V. 1.007.1/B 16/(1)068252190000818, V. 2.007.1/B 16068252194006451 -
v. 1 : gw2088002913,
v. 2 : gw2090004300, v. 1418.6/B051/12088002913, v. 2418.6/B051/22090004300 -
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references and indexes
内容説明・目次
- 巻冊次
-
v. 1 : gw ISBN 9783540186229
内容説明
This is the first of two volumes which present, in a systematic manner, the various areas of research in the field of structural complexity. Since the achievement of a formal definition of the concept of "algorithm," the Mathematical Theory of Computation has developed into a broad and rich discipline. The notion of "complexity of an algorithm" yields an important area of research, known as Complexity Theory, that can be approached from several points of view. The present Volume I is written in a style appropriate for undergraduate students who have taken a first course in Formal Language Theory. The first two chapters of this volume present the basic concepts of structural complexity, providing the background necessary for the understanding of complexity theory. Volume II will be addressed to graduate students and researchers. Both volumes are written in a textbook style; they contain about 200 exercises. The readers are led to a point where very little additional work will enable them to start research projects. In order to ease this step, an effort has been made to point out the main references for each of the results presented in the text.
- 巻冊次
-
v. 2 : gw ISBN 9783540520795
内容説明
This is the second volume of a systematic two-volume presentation of the various areas of research in the field of structural complexity. The mathematical theory of computation has developed into a broad and rich discipline within which the theory of algorithmic complexity can be approached from several points of view. This volume is addressed to graduate students and researchers and assumes knowledge of the topics treated in the first volume but is otherwise nearly self-contained. Topics covered include vector machines, parallel computation, alternation, uniform circuit complexity, isomorphism, biimmunity and complexity cores, relativization and positive relativization, the low and high hierarchies, Kolmogorov complexity and probability classes. Numerous exercises and references are given.
- 巻冊次
-
v. 2 : [pbk] ISBN 9783642753596
内容説明
This is the second volume of a two volume collection on Structural Complexity. This volume assumes as a prerequisite knowledge about the topics treated in Volume I, but the present volume itself is nearly self-contained. As in Volume I, each chapter of this book ends with a section entitled "Bibliographical Remarks", in which the relevant references for the chapter are briefly commented upon. These sections might also be of interest to those wanting an overview of the evolution of the field, as well as relevant related results which are not included in the text. Each chapter includes a section of exercises. The reader is encouraged to spend some time on them. Some results presented as exercises are occasionally used later in the text. A reference is provided for the most interesting and for the most useful exercises. Some exercises are marked with a * to indicate that, to the best knowledge of the authors, the solution has a certain degree of difficulty. Many topics from the field of Structural Complexity are not treated in depth, or not treated at all. The authors bear all responsibility for the choice of topics, which has been made based on the interest of the authors on each topic. Many friends and colleagues have made suggestions or corrections. In partic ular we would like to express our gratitude to Richard Beigel, Ron Book, Rafael Casas, Jozef Gruska, Uwe Schoning, Pekka Orponen, and Osamu Watanabe.
目次
1 Vector Machines.- 1.1 Introduction.- 1.2 Vector Machines: Definition and Basic Properties.- 1.3 Elementary Matrix Algebra on Vector Machines.- 1.4 Relation Between Vector Machines and Turing Machines.- 1.5 Exercises.- 1.6 Bibliographical Remarks.- 2 The Parallel Computation Thesis.- 2.1 Introduction.- 2.2 An Array Machine: the APM.- 2.3 A Multiprocessor Machine: the SIMDAG.- 2.4 A Tree Machine: the k-PRAM.- 2.5 Further Parallel Models.- 2.6 Exercises.- 2.7 Bibliographical Remarks.- 3 Alternation.- 3.1 Introduction.- 3.2 Alternating Turing Machines.- 3.3 Complexity Classes for Alternation.- 3.4 Computation Graphs of a Deterministic Turing Machine.- 3.5 Determinism Versus Nondeterminism for Linear Time.- 3.6 Exercises.- 3.7 Bibliographical Remarks.- 4 Uniform Circuit Complexity.- 4.1 Introduction.- 4.2 Uniform Circuits: Basic Definitions.- 4.3 Relationship with General-Purpose Parallel Computers.- 4.4 Other Uniformity Conditions.- 4.5 Alternating Machines and Uniformity.- 4.6 Robustness of NC and Conclusions.- 4.7 Exercises.- 4.8 Bibliographical Remarks.- 5 Isomorphism and NP-completeness.- 5.1 Introduction.- 5.2 Polynomial Time Isomorphisms.- 5.3 Polynomial Cylinders.- 5.4 Sparse Complete Sets.- 5.5 Exercises.- 5.6 Bibliographical Remarks.- 6 Bi-Immunity and Complexity Cores.- 6.1 Introduction.- 6.2 Bi-Immunity, Complexity Cores, and Splitting.- 6.3 Bi-Immune Sets and Polynomial Time m-Reductions.- 6.4 Complexity Cores and Polynomial Time m-Reductions.- 6.5 Levelability, Proper Cores, and Other Properties.- 6.6 Exercises.- 6.7 Bibliographical Remarks.- 7 Relativization.- 7.1 Introduction.- 7.2 Basic Results.- 7.3 Encoding Sets in NP Relativized.- 7.4 Relativizing Probabilistic Complexity Classes.- 7.5 Isolating the Crucial Parameters.- 7.6 Refining Nondeterminism.- 7.7 Strong Separations.- 7.8 Further Results in Relativizations.- 7.9 Exercises.- 7.10 Bibliographical Remarks.- 8 Positive Relativizations.- 8.1 Introduction.- 8.2 A Positive Relativization of the $$P\mathop = \limits^? PSPACE$$ Problem.- 8.3 A Positive Relativization of the $$NP\mathop = \limits^? PSPACE$$ Problem.- 8.4 A Positive Relativization of the $$P\mathop = \limits^? NP$$ Problem.- 8.5 A Relativizing Principle.- 8.6 Exercises.- 8.7 Bibliographical Remarks.- 9 The Low and the High Hierarchies.- 9.1 Introduction.- 9.2 Definitions and Characterizations.- 9.3 Relationship with the Polynomial Time Hierarchy.- 9.4 Some Classes of Low Sets.- 9.5 Oracle-Restricted Positive Relativizations.- 9.6 Lowness Outside NP.- 9.7 Exercises.- 9.8 Bibliographical Remarks.- 10 Resource-Bounded Kolmogorov Complexity.- 10.1 Introduction.- 10.2 Unbounded Kolmogorov Complexity.- 10.3 Resource-Bounded Kolmogorov Complexity.- 10.4 Tally Sets, Printability, and Ranking.- 10.5 Kolmogorov Complexity of Characteristic Functions.- 10.6 Exercises.- 10.7 Bibliographical Remarks.- 11 Probability Classes and Proof-Systems.- 11.1 Introduction.- 11.2 Interactive Proof-Systems: Basic Definitions and Examples.- 11.3 Arthur Against Merlin Games.- 11.4 Probabilistic Complexity Classes and Proof-Systems.- 11.5 Equivalence of AM and IP.- 11.6 Exercises.- 11.7 Bibliographical Remarks.- Appendix: Complementation via Inductive Counting.- 1 Nondeterministic Space is Closed Under Complement.- 2 Bibliographical Remarks.- References.- Author Index.- Symbol Index.
「Nielsen BookData」 より
