Course Overview and Formal Definition of Computation
1:19:32Turing Machines
1:19:47Simulations and Turing Machine Variants
1:20:14Time Complexity and Universal Turing Machines
1:17:57Time Hierarchy Theorem
1:20:50Problems in P
1:21:42SAT
1:20:28NP
1:21:04Nondeterminism
1:21:02Reductions
1:21:41NP-Completeness and the Cook-Levin Theorem
1:16:03NP-Completeness Reductions
1:20:32Search-to-Decision, Padding, Dichotomy Theorems
1:19:56Ladner's Theorem and Mahaney's Theorem
1:22:37coNP
1:21:29Space Complexity
1:21:12Savitch's Theorem and NL
1:21:12NL-Completeness and Logspace Reductions
1:20:21From P-Completeness to PSPACE-Completeness
1:19:39The Immerman-Szelepcsényi Theorem
1:21:05Savitch's Theorem and NL
This lecture explores Savitch's Theorem, establishing a fundamental relationship between deterministic and non-deterministic space complexity, and introduces the class NL.
Undergraduate Computational Complexity Theory
Lecture 17: Savitch's Theorem and NL
Carnegie Mellon Course 15-455, Spring 2017