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This graduate lecture introduces the polynomial-time hierarchy in computational complexity theory. It develops quantified-circuit and alternating-machine definitions, examines complexity classes and collapse questions, and relates the hierarchy to P versus NP.
Syllabus
Introduction
Polynomial Time Hierarchy
Quantifying over circuits
Defining complexity classes
Examples
Complexity Classes
There exists for all P
min circuit problem
min popular hypothesis
min unsurprising observation
min alternation
Taught by
Ryan O'Donnell