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545Re: [aima-talk] Formula for lookup table size on page 45

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  • The Geek
    Sep 20, 2005
    • 0 Attachment
      I'm not sure if you're being consistent in your
      definition of P, the possible precepts, since I can't
      figure out how you arrived at 15. (I agree with 39).

      To make life easy, assume you have a single sensor
      which can return one of three values - A, B, or C.
      The possible precept combinations can therefore be
      enumerated as:

      A
      B
      C
      AA
      AB
      AC
      BA
      BB
      BC
      ...
      AAA
      AAB
      AAC
      ABA
      ...

      I think you'll find (as the formula implies) there are
      3 possible combinations after the first input is
      received (t=1), there are 3^3 = 9 additonal
      combinations when the second input is received (t=2),
      and 3^3^3 additional combinations once the 3rd input
      is received (t=3). Add them all together, and you can
      see the agent would need a total of 39 table entries
      to know what action to take based on it's precept
      history.

      Rob G.

      --- kindlencotech <fredkindl@...> wrote:

      > To try and understand this equation I assumed the
      > following:
      > number of possible percepts P = 3
      > lifetime of the agent (number of percepts it will
      > receive) = 3
      > I the get an answer for the summation of 39.
      > However, if I manually
      > determine the number of possible ways in which the
      > percepts can be
      > received I get 15 for the size of the lookup table.
      > Can somebody tell
      > me what I am not undestanding correctly?
      >
      > Fred Kindl
      > fredkindl@...
      >
      >
      >
      >
      >
      >


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