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MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube ...
YouTube-MIT OpenCourseWare
Space Complexity Measures
PSPACE-Completeness Review
Recursive Solutions
Clarifying Questions
Each Recursive Level Stores One Configuration
F(n) - Number of States
Why Polynomial Time Reductibility?
Proof of PSPACE-Completeness
Semantics of PSPACE-Completeness
Exercise Solution
Here we introduce the notion of polynomial space and PSPACE-completeness, which is the same as NP-completeness except the language has to be ...
YouTube-Easy Theory
What is polynomial space
Why study polynomial space?
How to Prove PSPACE-Complete
What is PSPACE-Hard?
Is PSPACE a subset of NP?
MIT 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs, Fall 2014 View the complete course: http://ocw.mit.edu/6-890F14 Instructor: ...
Boulder Dash First Star Software, 1984
Boulder Dash is NP-hard Viglietta 2012
Zelda II is NP-hard
Pac-Man is NP-hard
Quake [id Software 1996]
Prince of Persia Brederbund 1989
Textbooks: Computational Complexity: A Modern Approach by S. Arora and B. Barak. Algorithm Design by J. Kleinberg and E. Tardos.
YouTube-Computer Science Theory Explained
What is space?
P is contained in PSPACE
Example of a turing machine
Satisfability in Polynomial Space
Enumeration example
Evaluating the formula
The n-bit odometer
All of NP is in PSPACE
Why NP is in PSPACE
How to decide if a word is in a language
SPACE COMPLEXITY - DSPACE, NSPACE, PSPACE, NPSPACE. 4.1K views · 3 years ago ...more. Learn IT easy with Mehbooba. 1.59K.
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00:00 - Introduction 00:54 - Formula-Game is PSPACE Complete 12:40 - Generalised-Geography is PSPACE Complete 21:45 - Generalised Games.
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Introduction
Formula-Game is PSPACE Complete
Generalised-Geography is PSPACE Complete
Generalised Games
Variable assignment tree
Evaluating the tree
Computing QSAT in polynomial space
Space Claim
Computing the solution
Space Usage
Evaluating the formula in the right subtree
Space requirements
Inductive step
Conclusion
Space Complexity Classes
Space Complexity: Number of States
Polynomial Time Reduction
How do we know that CoP is a complete class of problems?
Quantified Boolean Formulas (QBFs)
Why is SAT in PSPACE?
CONP completeness
Ladder Notation
Complement of a language in PSPACE
A discussion of the basic bounds on relating time and space complexity classes. Savitch's theorem and why PSPACE = NPSPACE.
YouTube-C. Seshadhri
L and NL spaces
Space-bounded machine: vertex set
Configuration graph
NP is in PSPACE
What is Savitch's theorem?
Logical formulation
Recursion Depth
Recurrence for SP(i)
Running time analysis
Definition of PSPACE-complete
Examples of PSPACE-complete problems
Extime
Polynomial spaces
Computing the number of configurations
What happens if the same configuration is encountered twice?
Summary
Computational complexity: Prove IP is subset of PSPACE 0:00 start 6:00 Prove IP is subset of PSPACE More computational complexity theory: ...
YouTube-Math Geeks
start
Prove IP is subset of PSPACE
General strategy for showing PSPACE-completeness
Competitive Facility Location can be solved in polynomial space
Reduction of Competitive Facility Location to QSAT
Reduction to QSAT
Graph construction
Optimal strategy
Competitive Facility Location: Objective Function
Undergraduate Computational Complexity Theory Lecture 25: Interactive Proofs: IP=PSPACE Carnegie Mellon Course 15-455, ...
YouTube-Ryan O'Donnell
Interactive Proofs
Proof systems
Basic properties of a proof system
Is this problem in P?
Basic Facts about IP
Best Prover Strategy
Simplest language in PSPACE
3-CNF proof sketch
Conversation between verifier and proofer
Degree 3M polynomials
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Chapter outline
Space as a computational resource
Definition of PSPACE
PSPACE and other classes of problems
Implementation in Polynomial Space
Basic Complexity class: P, NP, PSPACE, and EXP 0:00 start 1:00 definition of P 4:56 definition of NP 9:50 definition of PSPACE 10:30 prove P ...
definition of P
definition of NP
definition of PSPACE
prove P is a subset of NP
definition of EXP
prove that PSPACE is a subset of EXP
introduce TQBF and prove it is PSPACE
In which we show the proof that TQBF is PSPACE-complete, and prove the space hierarchy theorem. Hit the bell next to Subscribe so you ...
YouTube-Ryan Dougherty
PSPACE-completeness
TQBF: Totally Quantified Boolean Formula
Quantified boolean formulas
Sketch of proof that TQBF is PSPACE-hard
Space Hierarchy Theorem
Computing f(n)
Comments9. Nora Almayouf. Can I ask question about CFG, The set of production rules for CFG , is regular expression ?
YouTube-Unacademy Computer Science
Complexity Chain
What is L Space?
What is PSPACE and Logarithmic Space
Polynomial Space (PSPACE)
Examples of PSPACE
Exploring a significant breakthrough in theoretical quantum information research, "QIP=PSPACE," featuring researcher John Watrous of the ...
YouTube-Institute for Quantum Computing
If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 PSPACE ...
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... PSPACE class, where problems are solvable in polynomial space. Within this realm, the ... #PSPACE, #ParallelComputation, #PvsNP, #NPSPACE ...
YouTube-Mohammad Hajiaghayi
Introduction to Complexity
Negative Weights Cycle Problem
Tetris
Halting Problem
Meaning of the Certificate
Showing the Problem Is in Np
Coloring Problem
Definition of Np
Assumptions and Reductions
Rush Hour Problem