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Introduction to research in computational complexity theory. Computational models: nondeterministic, alternating, and probabilistic machines. Boolean circuits. Complexity classes associated with these models: NP, Polynomial hierarchy, BPP, P/poly, etc. Complete problems. Interactive proof systems and probabilistically checkable proofs: IP=PSPACE and NP=PCP (log n, l). Definitions of randomness. Pseudorandomness and derandomizations. Lower bounds for concrete models such as algebraic decision trees, bounded-depth circuits, and monotone circuits.