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Complexity Theory Companion Softcover reprint of hardcover 1st ed. 2002 [Mīkstie vāki]

  • Formāts: Paperback / softback, 372 pages, height x width: 235x155 mm, weight: 593 g, XIII, 372 p., 1 Paperback / softback
  • Sērija : Texts in Theoretical Computer Science. An EATCS Series
  • Izdošanas datums: 15-Dec-2010
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642086845
  • ISBN-13: 9783642086847
  • Mīkstie vāki
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  • Formāts: Paperback / softback, 372 pages, height x width: 235x155 mm, weight: 593 g, XIII, 372 p., 1 Paperback / softback
  • Sērija : Texts in Theoretical Computer Science. An EATCS Series
  • Izdošanas datums: 15-Dec-2010
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642086845
  • ISBN-13: 9783642086847
The Complexity Theory Companion is an accessible, algorithmically oriented, research-centered, up-to-date guide to some of the most interesting techniques of complexity theory.



The book's thesis is that simple algorithms are at the heart of complexity theory. From the tree-pruning and interval-pruning algorithms that shape the first chapter to the query simulation procedures that dominate the last chapter, the central proof methods of the book are algorithmic. And to more clearly highlight the role of algorithmic techniques in complexity theory, the book is - unlike other texts on complexity - organized by technique rather than by topic. Each chapter of this book focuses on one technique: what it is, and what results and applications it yields.





This textbook was developed at the University of Rochester in courses given to graduate students and advanced undergraduates. Researchers also will find this book a valuable source of reference due to the comprehensive bibliography of close to five hundred entries, the thirty-five page subject index, and the appendices giving overviews of complexity classes and reductions.

Recenzijas

From the reviews of the first edition:









"The introduction begins with two secrets: that algorithms are at the heart of complexity theory, and moreover that simple algorithms are at the heart of complexity theory. The main body of the book then proceeds to try and illustrate this view. While all the chapters primarily deal with a succession of theorems, lemmas and proofs, the surrounding text makes it fairly accessible and readable. The appendices are very well laid out and could probably replace a small library of textbooks." (A. Weaver, Journal of the Operational Research Society, Vol. 54, 2004)



"The book is intended for readers who seek an accessible, algorithmically oriented research-centered, up-to-date guide to several interesting techniques of computational complexity. In contrast to the organization of other books, each chapter of this book focuses on one particular technique in complexity theory. The book contains two appendices, the first presenting a concise overview on complexity classes, the second one on reductions. The book presents a survey on a great variety of recent interesting techniques in complexity." (Ludwig Staiger, Zentralblatt MATH, Vol. 993, 2002)

Papildus informācija

Springer Book Archives
Preface vii
Invitation vii
Usage viii
1 The Self-Reducibility Technique
1(30)
1.1 GEM: There Are No Sparse NP-Complete Sets Unless P=NP
2(16)
1.2 The Turing Case
18(4)
1.3 The Case of Merely Putting Sparse Sets in NP - P: The Hartmanis-Immerman-Sewelson Encoding
22(4)
1.4 OPEN ISSUE: Does the Disjunctive Case Hold?
26(1)
1.5 Bibliographic Notes
26(5)
2 The One-Way Function Technique
31(14)
2.1 GEM: Characterizing the Existence of One-Way Functions
32(3)
2.2 Unambiguous One-Way Functions Exist If and Only If Bounded-Ambiguity One-Way Functions Exist
35(1)
2.3 Strong, Total, Commutative, Associative One-Way Functions Exist If and Only If One-Way Functions Exist
36(6)
2.4 OPEN ISSUE: Low-Ambiguity, Commutative, Associative One-Way Functions?
42(1)
2.5 Bibliographic Notes
43(2)
3 The Tournament Divide and Conquer Technique
45(22)
3.1 GEM: The Semi-feasible Sets Have Small Circuits
45(3)
3.2 Optimal Advice for the Semi-feasible Sets
48(8)
3.3 Unique Solutions Collapse the Polynomial Hierarchy
56(7)
3.4 OPEN ISSUE: Are the Semi-feasible Sets in P/linear?
63(1)
3.5 Bibliographic Notes
63(4)
4 The Isolation Technique
67(24)
4.1 GEM: Isolating a Unique Solution
68(4)
4.2 Toda's Theorem: PH PPP
72(10)
4.3 NL/poly = UL/poly
82(5)
4.4 OPEN ISSUE: Do Ambiguous and Unambiguous Nondeterminism Coincide?
87(1)
4.5 Bibliographic Notes
87(4)
5 The Witness Reduction Technique
91(18)
5.1 Framing the Question: Is #P Closed Under Proper Subtraction?
91(2)
5.2 GEM: A Complexity Theory for Feasible Closure Properties of #P
93(6)
5.3 Intermediate Potential Closure Properties
99(4)
5.4 A Complexity Theory for Feasible Closure Properties of OptP
103(2)
5.5 OPEN ISSUE: Characterizing Closure Under Proper Decrement
105(1)
5.6 Bibliographic Notes
106(3)
6 The Polynomial Interpolation Technique
109(58)
6.1 GEM: Interactive Protocols for the Permanent
110(9)
6.2 Enumerators for the Permanent
119(3)
6.3 IP = PSPACE
122(11)
6.4 MIP = NEXP
133(30)
6.5 OPEN ISSUE: The Power of the Provers
163(1)
6.6 Bibliographic Notes
163(4)
7 The Nonsolvable Group Technique
167(30)
7.1 GEM: Width-5 Branching Programs Capture Nonuniform-NC1
168(8)
7.2 Width-5 Bottleneck Machines Capture PSPACE
176(5)
7.3 Width-2 Bottleneck Computation
181(11)
7.4 OPEN ISSUE: How Complex Is Majority-Based Probabilistic Symmetric Bottleneck Computation?
192(1)
7.5 Bibliographic Notes
192(5)
8 The Random Restriction Technique
197(38)
8.1 GEM: The Random Restriction Technique and a Polynomial-Size Lower Bound for Parity
197(10)
8.2 An Exponential-Size Lower Bound for Parity
207(11)
8.3 PH and PSPACE Differ with Probability One
218(4)
8.4 Oracles That Make the Polynomial Hierarchy Infinite
222(9)
8.5 OPEN ISSUE: Is the Polynomial Hierarchy Infinite with Probability One?
231(1)
8.6 Bibliographic Notes
231(4)
9 The Polynomial Technique
235(28)
9.1 GEM: The Polynomial Technique
236(5)
9.2 Closure Properties of PP
241(11)
9.3 The Probabilistic Logspace Hierarchy Collapses
252(7)
9.4 OPEN ISSUE: Is PP Closed Under Polynomial-Time Turing Reductions?
259(1)
9.5 Bibliographic Notes
260(3)
A A Rogues' Gallery of Complexity Classes
263(42)
A.1 P: Determinism
264(2)
A.2 NP: Nondeterminism
266(2)
A.3 Oracles and Relativized Worlds
268(2)
A.4 The Polynomial Hierarchy and Polynomial Space: The Power of Quantifiers
270(4)
A.5 E, NE, EXP, and NEXP
274(2)
A.6 P/Poly: Small Circuits
276(1)
A.7 L, NL, etc.: Logspace Classes
277(2)
A.8 NC, AC, LOGCFL: Circuit Classes
279(2)
A.9 UP, FewP, and US: Ambiguity-Bounded Computation and Unique Computation
281(5)
A.10 #P: Counting Solutions
286(2)
A.11 ZPP, RP, coRP, and BPP: Error-Bounded Probabilism
288(2)
A.12 PP, C = P, and SPP: Counting Classes
290(1)
A.13 FP, NPSV, and NPMV: Deterministic and Nondeterministic Functions
291(3)
A.14 P-Sel: Semi-feasible Computation
294(3)
A.15 P, ModkP: Modulo-Based Computation
297(1)
A.16 SpanP, OptP: Output-Cardinality and Optimization Function Classes
297(2)
A.17 IP and MIP: Interactive Proof Classes
299(1)
A.18 PBP, SF, SSF: Branching Programs and Bottleneck Computation
300(5)
B A Rogues' Gallery of Reductions
305(4)
B.1 Reduction Definitions: ≤pm, ≤pT
305(2)
B.2 Shorthands: R and E
307(1)
B.3 Facts about Reductions
307(1)
B.4 Circuit-Based Reductions: NCk and ACk
308(1)
B.5 Bibliographic Notes
308(1)
References 309(26)
Index 335