* Compilation of the most glorious episodes from the annals of theoretical computer science * Over 240 fascinating exercises with elegant solutions on the centrals themes of theoretical computer science
This book assembles some of the most important problems and solutions in theoretical computer science-from computability, logic, circuit theory, and complexity. The book presents these important results with complete proofs in an understandable form. It also presents previously open problems that have found (perhaps unexpected) solutions, and challenges the reader to pursue further active research in computer science.|While I was visiting Boston University during the 1996-97 academic year, I noticed a small book, written in German, on a shelf in Steve Homer's office. Curious, I borrowed it for my train ride home and began reading one of the chapters. I liked the style and format of the book so much that over the course of the next few months I frequently found myself reaching for it and working through one chapter or another. This was my introduction to Peden der Theoretischen Informatik. A few of my colleagues had also seen the book. They also found it inter esting, but most of them did not read German well enough to read more than small portions of it enjoyably. I hope that the English version will rectify this situation, and that many will enjoy (and learn from) the English version as much as I enjoyed the German version. The front matter of this book says that it has been "translated, revised, and expanded." I should perhaps say a few words about each of these tasks. In translating the book, I have tried as much as possible to retain the feel of the original, which is somewhat less formal and impersonal than a typical text book yet relatively concise. I certainly hope that the "pleasure of the pursuit of understanding" has not gotten lost in the translation.
The Priority Method.- Hilbert's Tenth Problem.- LOOP Programs.- Bottom Drawers for Resolution Proofs.- The Spectral Problem.- Kolmogorov Complexity.- Circuits for the Parity Function.- PAC Learning.- The Berman-Hartmanis Conjecture.- Collaborating Hierarchies.- Equivalence of Branching Programs.- Craig Interpolants.- Probability Amplification.- Interactive Proof Systems.- Zero Knowledge.- Graph Isomorphism.- Superconcentrations.- Pebble Game.
This book introduces some of the most important results in theoretical computer science. The "gems" are central problems and their solutions from the areas of computability, logic, circuit theory, and complexity. The text presents complete proofs in understandable form, as well as previously open problems that have found a (perhaps unexpected) solution, complex proofs from bottom drawers, probabilistic constructions, and much, much more. With over 240 intriguing exercises (elegant solutions for which are supplied), the text also challenges the reader to do some active work.
While I was visiting Boston University during the 1996-97 academic year, I noticed a small book, written in German, on a shelf in Steve Homer's office. Curious, I borrowed it for my train ride home and began reading one of the chapters. I liked the style and format of the book so much that over the course of the next few months I frequently found myself reaching for it and working through one chapter or another. This was my introduction to Peden der Theoretischen Informatik. A few of my colleagues had also seen the book. They also found it inter esting, but most of them did not read German well enough to read more than small portions of it enjoyably. I hope that the English version will rectify this situation, and that many will enjoy (and learn from) the English version as much as I enjoyed the German version. The front matter of this book says that it has been "translated, revised, and expanded." I should perhaps say a few words about each of these tasks. In translating the book, Ihave tried as much as possible to retain the feel of the original, which is somewhat less formal and impersonal than a typical text book yet relatively concise. I certainly hope that the "pleasure of the pursuit of understanding" has not gotten lost in the translation.
Fundamental Definitions and Results.- 1. The Priority Method.- 2. Hilbert's Tenth Problem.- 3. The Equivalence Problem for LOOP(l)- and LOOP(2)-Programs.- 4. The Second LBA Problem.- 5. LOGSPACE, Random Walks onGraphs, and Universal Traversal Sequences.- 6. Exponential Lower Bounds for the Length of Resolution Proofs.- 7. Spectral Problems and Deillegalscriptive Complexity Theory.- 8. Kolmogorov Complexity, the Universal Distribution, and Worst-Case vs. Average-Case.- 9. Lower Bounds via Kolmogorov Complexity.- 10. PAC-Learning and Occam's Razor.- 11. Lower Bounds for the Parity Function.- 12. The Parity Function Again.- 13. The Complexity of Craig Interpolants Ill.- 14. Equivalence Problems and Lower Bounds for Branching Programs.- 15. The Berman-Hartmanis Conjecture and Sparse Sets.- 16. Collapsing Hierarchies.- 17. Probabilistic Algorithms, Probability Amplification, and the Recycling of Random Numbers.- 18. The BP Operator and Graph Isomorphism.- 19. The BP-Operator and the Power of Counting Classes.- 20. Interactive Proofs and Zero Knowledge.- 21. IP = PSPACE.- 22. P ? NP with probability 1.- 23. Superconcentrators and the Marriage Theorem.- 24. The Pebble Game.- 25. Average-Case Complexity.- 26. Quantum Search Algorithms.- Solutions.
Prof. Dr. Uwe Schöning ist Leiter der Abteilung Theoretische Informatik der Universität Ulm.
Inhaltsverzeichnis
The Priority Method.- Hilbert's Tenth Problem.- LOOP Programs.- Bottom Drawers for Resolution Proofs.- The Spectral Problem.- Kolmogorov Complexity.- Circuits for the Parity Function.- PAC Learning.- The Berman-Hartmanis Conjecture.- Collaborating Hierarchies.- Equivalence of Branching Programs.- Craig Interpolants.- Probability Amplification.- Interactive Proof Systems.- Zero Knowledge.- Graph Isomorphism.- Superconcentrations.- Pebble Game.
Klappentext
This book assembles some of the most important problems and solutions in theoretical computer science-from computability, logic, circuit theory, and complexity. The book presents these important results with complete proofs in an understandable form. It also presents previously open problems that have found (perhaps unexpected) solutions, and challenges the reader to pursue further active research in computer science.
Compilation of the most glorious episodes from the annals of theoretical computer science * Over 240 fascinating exercises with elegant solutions on the centrals themes of theoretical computer science
