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18.404J The Theory of Computation

18.404J/6.840J The Theory of Computation(Fall 2020, MIT OCW). Instructor: Prof. Michael Sipser. This course emphasizes computability and computational complexity theory. Topics include regular and context-free languages, decidable and undecidable problems, reducibility, recursive function theory, time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems. (from ocw.mit.edu)

Introduction: Finite Automata, Regular Expressions


Lecture 01 - Introduction: Finite Automata, Regular Expressions
Lecture 02 - Nondeterminism, Closure Properties, Regular Expressions to Finite Automata
Lecture 03 - Regular Pumping Lemma, Finite Automata to Regular Expressions
Lecture 04 - Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion
Lecture 05 - CF Pumping Lemma, Turing Machines
Lecture 06 - TM Variants, Church-Turing Thesis
Lecture 07 - Decision Problems for Automata and Grammars
Lecture 08 - Undecidability
Lecture 09 - Reducibility
Lecture 10 - Computation History Method
Lecture 11 - Recursion Theorem and Logic
Lecture 12 - Time Complexity
Lecture 13
Lecture 14 - P and NP, SAT, Poly-Time Reducibility
Lecture 15 - NP-Completeness
Lecture 16 - Cook-Levin Theorem
Lecture 17 - Space Complexity, PSPACE, Savitch's Theorem
Lecture 18 - PSPACE-Completeness
Lecture 19 - Games, Generalized Geography
Lecture 20 - L and NL, NL = coNL
Lecture 21 - Hierarchy Theorems
Lecture 22 - Provably Intractable Problems, Oracles
Lecture 23 - Probabilistic Computation, BPP
Lecture 24 - Probabilistic Computation (cont.)
Lecture 25 - Interactive Proof Systems, IP
Lecture 26 - coNP is a subset of IP

References
18.404J/6.840J The Theory of Computation (Fall 2020)
Instructor: Prof. Michael Sipser. Lecture Notes. Assignments: Problem Sets (No Solutions). Exams (No Solutions). This course emphasizes computability and computational complexity theory.