Book contents
- Frontmatter
- Contents
- Preface
- Organization and Chapter Summaries
- Notation
- Acknowledgments
- 1 The Main Themes: Approximate Decision and Sublinear Complexity
- 2 Testing Linearity (Group Homomorphism)
- 3 Low-Degree Tests
- 4 Testing Monotonicity
- 5 Testing Dictatorships, Juntas, and Monomials
- 6 Testing by Implicit Sampling
- 7 Lower Bounds Techniques
- 8 Testing Graph Properties in the Dense Graph Model
- 9 Testing Graph Properties in the Bounded-Degree Graph Model
- 10 Testing Graph Properties in the General Graph Model
- 11 Testing Properties of Distributions
- 12 Ramifications and Related Topics
- 13 Locally Testable Codes and Proofs
- Appendix A Probabilistic Preliminaries
- Appendix B A Mini-Compendium of General Results
- Appendix C An Index of Specific Results
- References
- Index
Appendix C - An Index of Specific Results
Published online by Cambridge University Press: 13 November 2017
- Frontmatter
- Contents
- Preface
- Organization and Chapter Summaries
- Notation
- Acknowledgments
- 1 The Main Themes: Approximate Decision and Sublinear Complexity
- 2 Testing Linearity (Group Homomorphism)
- 3 Low-Degree Tests
- 4 Testing Monotonicity
- 5 Testing Dictatorships, Juntas, and Monomials
- 6 Testing by Implicit Sampling
- 7 Lower Bounds Techniques
- 8 Testing Graph Properties in the Dense Graph Model
- 9 Testing Graph Properties in the Bounded-Degree Graph Model
- 10 Testing Graph Properties in the General Graph Model
- 11 Testing Properties of Distributions
- 12 Ramifications and Related Topics
- 13 Locally Testable Codes and Proofs
- Appendix A Probabilistic Preliminaries
- Appendix B A Mini-Compendium of General Results
- Appendix C An Index of Specific Results
- References
- Index
Summary
Summary: This appendix provides an index to all results regarding specific properties that were presented in this book. For each property, we provide references only to the sections (or statements) in which relevant results can be found.
The properties are partitioned into five main groups, whereas in each group the listing is by alphabetic order. The first list contains all properties of objects that are most naturally described as functions or sequences. The next three lists refer to the three models of testing graph properties, which were studied in Chapters 8–10. The last list refers to properties of distributions, which were studied in Chapter 11.
Properties of Functions. Such properties were studied mostly in Chapters 2–6.
affine functions: Last paragraph of Chapter 2.
affine subspaces: Section 5.2.2.2 as well as Exercises 5.9–5.11.
codewords: Chapter 13.
• For the Hadamard code see also linearity.
• For general linear codes see Proposition 1.11.
• For the Long Code see also dictatorship.
• For the Reed–Muller code see also low-degree polynomials.
dictatorship: Section 5.2.
homomorphism (a.k.a. group homomorphism): Chapter 2.
junta: Section 5.3 and Corollary 7.20.
linearity: Special case of homomorphism.
low-degree polynomials: Chapter 3.
majority: Proposition 1.1.
monomials: Section 5.2.2 as well as Corollaries 6.4 and 6.7.
monotonicity: Chapter 4. See also sorted.
proofs: Chapter 13.
sparse (low-degree) polynomials (and linear functions): Corollary 7.12.
sorted: Proposition 1.5 and 1.8. See also monotonicity.
Graph Properties (in the Dense Graph Model). All in Chapter 8.
biclique: Proposition 8.6.
bipartiteness: Section 8.3.1.
colorability (by fixed number of colors): Theorem 8.13.
degree regularity: Theorem 8.5.
induced subgraph freeness: Theorem 8.20.
max-clique: Special case of Theorem 8.12.
max-cut: Special case of Theorem 8.12.
min-bisection: Special case of Theorem 8.12.
subgraph freeness: Section 8.4.2.
Recall that properties of sparse graphs (e.g., planarity) and properties that are close to any graph (e.g., connectivity) are easy to test in this model.
Graph Properties (in the Bounded-Degree Graph Model). All in Chapter 9.
bipartiteness: Sections 9.3.1 and 9.4.1.
colorability (by three colors): Theorem 9.19.
connectivity: Section 9.2.3. See Section 9.2.4 for t-connectivity.
cycle-freeness: Section 9.2.5, Theorem 9.17, and Section 9.4.2.
degree regularity: Section 9.2.2.
Eulerian: See the last paragraph in Section 9.2.2 and the last paragraph in Section 9.2.3.
expansion: Theorem 9.18.
planarity: Special case of Theorem 9.25.
subgraph freeness: Theorem 9.4.
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- Information
- Introduction to Property Testing , pp. 427 - 428Publisher: Cambridge University PressPrint publication year: 2017