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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)

Lecture 18 - PSPACE-Completeness

Quickly reviewed last lecture. Proved Savitch's Theorem: NSPACE (f(n)) ⊆ SPACE (f²(n)). Also proved PSPACE-completeness and TQBF is PSPACE-complete.

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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