Spring 2023

Carnegie Mellon University

This course provides an initial dive into complexity theory, exploring computations bound by resources like time, space, and energy. Emphasis is placed on low complexity classes.

This course provides a gentle introduction into complexity theory, the theory of computations that are restricted by various resource bounds (time, space, energy, ...). We start with a brief tour of the computational universe at large and then home in on the low complexity classes that are most relevant in theoretical computer science such as P, NP, PSPACE. LOG,NLOG, BPP, RP and circuit-based classes.

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Circuit ComplexityCompletenessComplexity TheoryComputabilityCook-Levin TheoremCountingDescriptive complexity theoryFundamental ResultsHardnessHypercomputationImmerman–Szelepcsényi theoremInteractive ProofsKarp's ListKolmogorov complexityLadner's TheoremNondeterminismP/NPPolynomial HierarchyPolynomial SpacePolynomial TimeProbabilistic ClassesRandomized AlgorithmsRandomnessReversible ComputationSatisfiabiltySmalll SpaceSpace ComplexityTime ComplexityTuring Machines