Introduction, Finite Automata, Regular Expressions
1:00:34Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA
1:03:27Regular Pumping Lemma, Conversion of FA to Regular Expressions
1:10:02Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion
1:09:22CF Pumping Lemma, Turing Machines
1:13:59TM Variants, Church-Turing Thesis
1:14:49Decision Problems for Automata and Grammars
1:16:51Undecidability
1:17:02Reducibility
1:16:37Computation History Method
1:21:41Recursion Theorem and Logic
1:17:32Time Complexity
1:25:37P and NP, SAT, Poly-Time Reducibility
1:19:23NP-Completeness
1:25:53Cook-Levin Theorem
1:18:27Space Complexity, PSPACE, Savitch's Theorem
1:20:10PSPACE-Completeness
1:17:36Games, Generalized Geography
1:19:38L and NL, NL = coNL
1:20:06Hierarchy Theorems
1:21:57Provably Intractable Problems, Oracles
1:22:50Probabilistic Computation, BPP
1:23:41P and NP, SAT, Poly-Time Reducibility
The lecture defines NTIME(t(n)) classes and NP, proving COMPOSITES is in NP. It discusses the P vs. NP problem, establishes that CFG acceptance is in P, and introduces SAT and polynomial-time reducibility.
MIT 18.404J Theory of Computation, Fall 2020
Instructor: Michael Sipser
View the complete course: https://ocw.mit.edu/18-404JF20
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY