another theory of computation problem

This is a discussion on another theory of computation problem within the A Brief History of Cprogramming.com forums, part of the Community Boards category; well I'm kind-of stuck on this question: Let ALL DFA = { <A> | A is a DFA that recognizes ...

  1. #1
    Registered User axon's Avatar
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    another theory of computation problem

    well I'm kind-of stuck on this question:

    Let ALL DFA = { <A> | A is a DFA that recognizes ∑* }. Show that ALL DFA is decidable.

    I have to prove this two different ways. So far I figured out one, and can't think of any other way...any ideas?

    here is the first solution:
    ______
    ALL DFA == E DFA, we know that E DFA is decidable (theorem 4.4) and since decidable languages are closed under the comlpement operation, ALL DFA is decidable.

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

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    I really wish I knew what you were talking about, seems cool.
    See you in 13

  3. #3
    Registered User axon's Avatar
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    >>I really wish I knew what you were talking about, seems cool.<<

    THanks for letting me know!

    it is cool, but quite complicated - esspecially when you're taking 18 credit hours in total.

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

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    Mayor of Awesometown Govtcheez's Avatar
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    > it is cool, but quite complicated - esspecially when you're taking 18 credit hours in total.

    Wuss - we had to take 20 almost every term.

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    Bob Dole for '08 B0bDole's Avatar
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    >Wuss - we had to take 20 almost every term.

    full time is 12 :-/
    Hmm

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    geek SilentStrike's Avatar
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    What is E DFA?
    Prove you can code in C++ or C# at TopCoder, referrer rrenaud
    Read my livejournal

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    geek SilentStrike's Avatar
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    Actually.. this is quite easy. Let A be a DFA (thought it was a PDA first.. that had me perplexed), we want to determine if L(A) = ∑*. L(A) = ∑* iff there is no string that results in a rejection state when ran on your DFA. But a DFA is just a finte directed graph. So you just do a graph search from the start node of A. If you hit a rejecting final state, L(A) != ∑*, otherwise, L(A) = ∑*.
    Prove you can code in C++ or C# at TopCoder, referrer rrenaud
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  8. #8
    Mayor of Awesometown Govtcheez's Avatar
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    Quote Originally Posted by B0bDole
    >Wuss - we had to take 20 almost every term.

    full time is 12 :-/
    Fulltime for us was 16

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    Quote Originally Posted by SilentStrike
    Actually.. this is quite easy. Let A be a DFA (thought it was a PDA first.. that had me perplexed), we want to determine if L(A) = ∑*. L(A) = ∑* iff there is no string that results in a rejection state when ran on your DFA. But a DFA is just a finte directed graph. So you just do a graph search from the start node of A. If you hit a rejecting final state, L(A) != ∑*, otherwise, L(A) = ∑*.
    Arg, well now that you put it THAT way it's obviously quite clearly an easy problem. Just take the result of that, divide it by the square root of the sine of PI times i raised to the negative infinity, plus 2...im so stoopid!

    I still really wish I knew what was going on...ill leave now
    See you in 13

  10. #10
    geek SilentStrike's Avatar
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    It's really not a hard concept if you understand the terminology and the symbols.

    This is a reasonably clear explanation of what DFAs are. You can get the picture and the example at the bottom, and then work back to the nasty definitions and such.

    http://www.cse.nd.edu/courses/cse411...des/lect04.pdf
    Prove you can code in C++ or C# at TopCoder, referrer rrenaud
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  11. #11
    Registered User axon's Avatar
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    er edit...kinda missed the other posts....

    I figured out the other solution - and yours doesn't work SilentStrike
    Last edited by axon; 11-12-2004 at 08:21 PM.

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

  12. #12
    Registered User axon's Avatar
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    >>Wuss - we had to take 20 almost every term<<
    >>Fulltime for us was 16<<

    maybe it was a different load then, or hours per class. My 18 hours = 6 three hour classes, which is a lot! actually its the most you can take without a petition.

    How much was your calculus worth? chem? phys? in hours, that is.

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

  13. #13
    Registered User axon's Avatar
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    yey for multiple posts!

    >>What is E DFA?<<

    the 'E' stands for emptiness; used for emptiness testing

    some entropy with that sink? entropysink.com

    there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka

  14. #14
    geek SilentStrike's Avatar
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    Why doesn't it work?
    Prove you can code in C++ or C# at TopCoder, referrer rrenaud
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