by Johan Håstad
Number of pages: 130
The main idea of the course has been to give the broad picture of modern complexity theory. To define the basic complexity classes, give some examples of each complexity class and to prove the most standard relations. The set of notes does not contain the amount of detail wanted from a text book. I have taken the liberty of skipping many boring details and tried to emphasize the ideas involved in the proofs. Probably in many places more details would be helpful and I would he grateful for hints on where this is the case. Most of the notes are at a fairly introductory level but some of the section contain more advanced material. This is in particular true for the section on pseudorandom number generators and the proof that IP = PSPACE. Anyone getting stuck in these parts of the notes should not be disappointed.
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by Luca Trevisan
Notes from a graduate courses on Computational Complexity. The first 15 lectures cover fundamentals, the remaining is advanced material: Hastad's optimal inapproximability results, lower bounds for parity in bounded depth-circuits, and more.
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These notes provide an introduction to the subject of measure-preserving dynamical systems, discussing the dynamical viewpoint; how and from where measure-preserving systems arise; the construction of measures and invariant measures; etc.
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Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of algorithmic randomness and complexity for scientists from diverse fields.
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Lecture notes for a graduate course on computational complexity taught at the University of Washington. Alternating Turing machines are introduced very early, and deterministic and nondeterministic Turing machines treated as special cases.