Computer Science Theory Explained
Computer Science Theory Explained
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Binary vs. Unary Number Encodings and Strong NP-completeness
Textbooks:
Computational Complexity: A Modern Approach by S. Arora and B. Barak.
Algorithm Design by J. Kleinberg and E. Tardos.
Lecture slides by K. Wayne accompanying the latter textbook:
www.cs.princeton.edu/~wayne/kleinberg-tardos/
Переглядів: 1 202

Відео

The Lemke-Howson Algorithm - Complementary Pivoting
Переглядів 3,4 тис.2 роки тому
The Lemke-Howson Algorithm - Complementary Pivoting
The Lemke-Howson Algorithm - Best Response Polytopes
Переглядів 2,9 тис.2 роки тому
The Lemke-Howson Algorithm - Best Response Polytopes
The Lemke-Howson Algorithm - Best Response Diagrams
Переглядів 4 тис.2 роки тому
The Lemke-Howson Algorithm - Best Response Diagrams
Colorability of Planar Graphs
Переглядів 1,4 тис.2 роки тому
Textbooks: Computational Complexity: A Modern Approach by S. Arora and B. Barak. Algorithm Design by J. Kleinberg and E. Tardos. Lecture slides by K. Wayne accompanying the latter textbook: www.cs.princeton.edu/~wayne/kleinberg-tardos/
The Complexity Class PPAD
Переглядів 1,3 тис.2 роки тому
The Complexity Class PPAD
Scarf's Theorem
Переглядів 5972 роки тому
Scarf's Theorem
Computing a Nash Equilibrium
Переглядів 1,2 тис.2 роки тому
Computing a Nash Equilibrium
Nash's Theorem
Переглядів 2,4 тис.2 роки тому
John Nash's PhD Thesis: library.princeton.edu/special-collections/sites/default/files/Non-Cooperative_Games_Nash.pdf
Brouwer's Fixed Point Theorem
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Brouwer's Fixed Point Theorem
Sperner's Lemma
Переглядів 4,3 тис.2 роки тому
Sperner's Lemma
Two-Player Zero-Sum - a Second Example
Переглядів 1,2 тис.2 роки тому
Two-Player Zero-Sum - a Second Example
Solving Rock-Paper-Scissors
Переглядів 6 тис.2 роки тому
Solving Rock-Paper-Scissors
Existence and Computation of Nash Equilibria in Two-Player Zero-Sum Games
Переглядів 1,7 тис.2 роки тому
Existence and Computation of Nash Equilibria in Two-Player Zero-Sum Games
A Brief Linear Programming Refresher
Переглядів 1,1 тис.2 роки тому
A Brief Linear Programming Refresher
Two-Player Zero-Sum Games
Переглядів 3,3 тис.2 роки тому
Two-Player Zero-Sum Games
The Poisened Drink and the Mixed Nash Equilibrium
Переглядів 1,1 тис.2 роки тому
The Poisened Drink and the Mixed Nash Equilibrium
The Battle of the Sexes and Burning Money
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The Battle of the Sexes and Burning Money
Pure Nash Equilibrium - a Further Example
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Pure Nash Equilibrium - a Further Example
The Battle of the Sexes
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The Battle of the Sexes
Weak Dominance
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Weak Dominance
The Iterated Elimination of Dominated Strategies
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The Iterated Elimination of Dominated Strategies
Dominating Strategies in the Prisoner's Dilemma
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Dominating Strategies in the Prisoner's Dilemma
The Prisoner's Dilemma
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The Prisoner's Dilemma
Games in Strategic Form
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Games in Strategic Form
The "Tragedy" in the Tragedy of the Commons
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The "Tragedy" in the Tragedy of the Commons
The Tragedy of the Commons
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The Tragedy of the Commons
Algorithmic Game Theory - Introduction
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Algorithmic Game Theory - Introduction
An FPTAS for the Knapsack Problem
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An FPTAS for the Knapsack Problem
Another Dynamic Program for the Knapsack Problem
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Another Dynamic Program for the Knapsack Problem

КОМЕНТАРІ

  • @shantanukaushikmathoholic
    @shantanukaushikmathoholic 10 днів тому

    Lf is basically how to define a set, for which the output is "yes".

  • @shantanukaushikmathoholic
    @shantanukaushikmathoholic 10 днів тому

    Sire, any book recommendation to along this playlist ?

  • @jasoncotton9804
    @jasoncotton9804 13 днів тому

    Wouldn't a set of non-result altering transformations which result in True be a verifiable certificate for the Tautology problem? Thanks for the well articulated video.

  • @cikechukwujohn
    @cikechukwujohn 16 днів тому

    Who is here in August, 2024. I am.

  • @akshatgupta7471
    @akshatgupta7471 Місяць тому

    can you pls proved the pdfs of your notes? they would be really helpful for revising the concepts

  • @akshatgupta7471
    @akshatgupta7471 Місяць тому

    thank you very much... this was really helpful :) would be great if you could provide the pdfs of your handwritten notes

  • @adrianho7165
    @adrianho7165 Місяць тому

    The first proof seems to be easier to come up with

  • @victornweze7230
    @victornweze7230 Місяць тому

    Hello @compscilessons Great work you are doing on this channel. I have a favour to ask of you. I have a paper on computational complexity, more specifically on SAT solving and would like a peer review. Unfortunately, I am unaffiliated with any institutions. Can you give me an endorsement on the preprint server arXiv so that I can make a submission or provide an email address where I can share my paper with you? Any assistance on this is appreciated. Thanks.

  • @dan7nm
    @dan7nm Місяць тому

    Really helpful thanks!

  • @MohdYaseenmas
    @MohdYaseenmas 2 місяці тому

    Thank you

  • @michaelperry886
    @michaelperry886 2 місяці тому

    Why is the g in the definition of a reduction taking in both of x and y?

  • @queenpost
    @queenpost 2 місяці тому

    Very clear explanation - Thanks! One Question: What would we do, if we insist, that the numbers given as instance for the SUBST SUM problem are different to each other?

    • @queenpost
      @queenpost 2 місяці тому

      O.K., the solution is given at the end!

  • @nicolasgioanni606
    @nicolasgioanni606 3 місяці тому

    No other video explains the pricing method on weighted vertex covers as well as yours, thank you so much, great video

  • @FabiolaMariaVillatoroGarcia
    @FabiolaMariaVillatoroGarcia 3 місяці тому

    You are genuinely awesome.

  • @halchen1439
    @halchen1439 3 місяці тому

    you are single handedly saving my ass. may your soul be blessed

  • @olxxa4967
    @olxxa4967 4 місяці тому

    Anyway, thank you. This video helped me a lot 🎉

  • @olxxa4967
    @olxxa4967 4 місяці тому

    Can you please do the colonel Blotto game

  • @nothingspecial2018
    @nothingspecial2018 4 місяці тому

    you did good job but my stoopid self could not understand it.

  • @ElIrracional
    @ElIrracional 4 місяці тому

    Why is that true? What about a clause of the form: x and ~y? It is not satistied when x and y are true and not satisfied when x and y are false.

  • @liamtolkkinen5025
    @liamtolkkinen5025 4 місяці тому

    you really don't explain things well

  • @welfarewagonrepairs
    @welfarewagonrepairs 4 місяці тому

    This was a very helpful explanation. The part after 13:00 was especially helpful explaining the purpose of the additional rows

  • @laautaro11
    @laautaro11 4 місяці тому

    Your channel is the best theoretical CS channel I've seen, fantastic job! thank you!

  • @lucasarif4387
    @lucasarif4387 4 місяці тому

    when you wrote down that proof idea at 2:30 my mouth started watering lets see where this goes

  • @lucasarif4387
    @lucasarif4387 4 місяці тому

    this module is so so good

  • @gate_dose
    @gate_dose 4 місяці тому

    Thank You!!

  • @user-uy1sl4sk3f
    @user-uy1sl4sk3f 4 місяці тому

    Thanks!

  • @user-rf4ue5kc3u
    @user-rf4ue5kc3u 5 місяців тому

    thank you so so so so much!!! you explain everything so clearly!!!!

  • @manawa3832
    @manawa3832 5 місяців тому

    i am going to now define the concept of mebeingfkingright. this foundational principle, now called mebeingfkingright, will be proven in the following way. i propose a machine, called the RightMachine that lays out a sequence of adjacent symbols. in each symbol is encoded the final position of the symbol to the left of itself or non at all. the machine beingfkingright at r0 and ends at r-finished. any sequence that this machine can lay down is said to be mebeingfkingright. therefore mebeingfkingright is any seqquence of symbols of mebeingfkingright that the RightMachine can process i.e. can go from r0-r-finish. tada the same level of proof as computability in this turing complete nonsense. the entire field of computer science folks.. like seriously without information theory and linguistics, computer science would just be a joke based on the inane crackpot nonsense of two guys during ww2.

  • @alieser7770
    @alieser7770 6 місяців тому

    Sir, you are doing God's work

  • @abdurrahmanyakar3040
    @abdurrahmanyakar3040 6 місяців тому

    Teacher, time 1:01, you write a f:{0,1}*: What does asterisk (*) mean?

    • @compscilessons
      @compscilessons 6 місяців тому

      The * is referred to as the Kleene star. {0,1}* is the set of all bitstrings of arbitrary (but finite) length. This includes the empty string, i.e., the string that has length 0.

  • @alexdolan9373
    @alexdolan9373 6 місяців тому

    Yup im bout to fail my exam lol

  • @EntertainmentUnit
    @EntertainmentUnit 7 місяців тому

    Was the question "What is Computation?" ever directly answered? Is a computation one run of a Turing machine from q_start to q_end? But even that doesn't answer the question, it only provides an example of a computation which is different than defining it.

  • @alexvisan7622
    @alexvisan7622 7 місяців тому

    Thank you!

  • @MarewanMahmud
    @MarewanMahmud 7 місяців тому

    Can u exaplian why (0,0,1) true but (0,1,0) false , plz i need u ?

    • @NittyLittyNiturzion
      @NittyLittyNiturzion 4 місяці тому

      this is just an example for an arbitrary formula, it's not the case that φ(0,0,1) = true and φ(0,1,0) = false in general

  • @and_I_am_Life_the_fixer_of_all
    @and_I_am_Life_the_fixer_of_all 7 місяців тому

    oh wow, thanks! big fan of this thesis! it does seem like we'll get computer simulations that you can't distinguish from reality one day!

  • @jasperdelandsheere5316
    @jasperdelandsheere5316 7 місяців тому

    Amazing work!

  • @yaras9648
    @yaras9648 7 місяців тому

    If K = 3 or generally > 2, can you still find a solution in polynomial time?

  • @xiaotaolee
    @xiaotaolee 7 місяців тому

    thank you ,do you have the code of the The List Scheduling Algorithm? if you have,can you share with me please.

  • @bytecode5834
    @bytecode5834 7 місяців тому

    This course is pure gold. Many thanks for your time and effort man

  • @nikonru3287
    @nikonru3287 8 місяців тому

    Really nice course, I watched it with interest and joy.

  • @markomekjavic
    @markomekjavic 8 місяців тому

    really well explained, thank you!

  • @awepossum1059
    @awepossum1059 8 місяців тому

    Hervorragend!

  • @anishajoshi3635
    @anishajoshi3635 8 місяців тому

    thanks, saving my grade fr <3

  • @user-wg5oq3xj5n
    @user-wg5oq3xj5n 8 місяців тому

    It’s been enjoyable journey into the Complexity theory. Thank you Matthias

  • @GodlyZara
    @GodlyZara 8 місяців тому

    best video out there for planar and graph color

  • @markomekjavic
    @markomekjavic 8 місяців тому

    simply amazing, your explanations are phenomenal

  • @user-hu7wu7py2o
    @user-hu7wu7py2o 9 місяців тому

    Amazing tutorial! Explained the concepts behind LH algorithms brilliantly

  • @jazibarehman6812
    @jazibarehman6812 9 місяців тому

    life saver

  • @its_just_brian8781
    @its_just_brian8781 9 місяців тому

    Why can't x1 and ~x2 both be green? Or red?

    • @allvarofarias
      @allvarofarias 4 місяці тому

      in this case the problem is that Xi and ~Xi have the same color, as this would not be consistent. In the case of a 3SAT problem formula, we must have at least one of the literals have the true value, therefore, I believe that nothing prevents it from having two true values ​​as long as they are not opposite literals. My english is very bad, sorry

  • @faridmusayev2587
    @faridmusayev2587 9 місяців тому

    Could you please explain why is there is a condition on T(n) >= n for all n in N in the second case for k-tape example?

    • @queenpost
      @queenpost 6 місяців тому

      Because the machine should be able to read the whole input.