Berkeley CSUA MOTD:Entry 30235
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2025/05/24 [General] UID:1000 Activity:popular
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2004/5/15 [Computer/SW/Languages, Computer/SW/OS/Windows] UID:30235 Activity:high
5/15    http://www.csua.berkeley.edu/~ilyas/problems/good_and_evil
        A classic theory problem cast in slightly theological terms. -- ilyas
        \_It's 2 in the morn. and i've had some sake, but this q. makes no
          sense to me.  Am i missing the definition of good and evil
          somewhere in there?
          \_ No.
        \_ Well in theological terms, anything that comes from Satan is of
           Satan and therefore evil.  All objects from Satan are evil.  No
           objects from Satan are good.  The correct answer in pseudo code is:
           while (getNextObjectFromSatan()) { print "Object is evil" }
        \_ Is this actually two questions? (1) a strategy for the man to be
           fooled about good objects no more than half the time, and (2)
           to "program a computer" to always be right?
           \_ No, you assume the man knows the strategy already, whatever it
              is, for S. -- ilyas
        \_ Once again, my problem with theory problems is figuring out
           what the heck they are talking about.
           \_ For this problem, substitute "ilyas" for "Satan", "theory
              problem" for "object", and "stupid" for "evil".  Then make
              ilyas' goal to convince you that the problems are good.
              The human wins when he realizes he's wasting his time.
                \- good one. if i were that witty, i'd have signed my post.
                   -- !sarcastic
                   \_ It would have detracted from the joke.  -tom
                      \_ Naturally.
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www.csua.berkeley.edu/~ilyas/problems/good_and_evil
Imagine two parties: a man and Satan playing the following game. The man is given objects, one at a time, and his job is to recognize if the object is good or evil. Satan's job is to make the man believe all objects are evil. Satan is omnipotent and can perform any computations he wishes, and always answers instantly. The man is mortal, his lifespan is a polynomial of the sizes of the objects he is dealing with. Thus, he is limited in the kinds of things he can compute, and how many questions he can ask Satan. The man can also flip coins, and since the coins are random and have no mind to be read, the results of the flips are unknown to Satan. We say the man wins the game (for some set of objects) if, whenever an object from the set is evil, the man always accepts it as evil. If the object is good, the man accepts it as evil (ie is fooled by Satan) no more than half the time. Assume the man can win the game with some set of objects S Describe how the man can program a computer to _always_ recognize objects from S as good and evil correctly, (without the aid of coins or Satan). The only restriction on the man's computer is that it cannot use more space than some polynomial of the size of the objects.