Explore the Polynomial Time Hierarchy in this graduate-level lecture on Computational Complexity Theory. Delve into advanced topics including quantifying over circuits, defining complexity classes, and examining examples. Learn about the "There exists for all P" concept, the min circuit problem, popular hypotheses, and unsurprising observations related to the hierarchy. Gain insights into alternation and its role in complexity theory. Part of Carnegie Mellon's Course 15-855 (Fall 2017), this lecture is taught by Ryan O'Donnell and includes suggested readings from Arora--Barak Chapters 5.1--5.3.
The Polynomial Time Hierarchy: Graduate Complexity Lecture at CMU
Overview
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
Related Courses
-
Computational Complexity
-
Circuits - Graduate Complexity Lecture 4 at CMU
-
Time-Space Tradeoffs for SAT - Graduate Complexity Lecture at CMU
-
Razborov-Smolensky Lower Bounds for AC0[p] - Graduate Complexity Lecture at CMU
-
Hierarchy Theorems - Time, Space, and Nondeterministic: Graduate Complexity Lecture at CMU
-
Approximate Counting - Graduate Complexity Lecture at CMU
