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Formula for lookup table size on page 45

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  • kindlencotech
    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
    Message 1 of 2 , Sep 18, 2005
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      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@...
    • The Geek
      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
      Message 2 of 2 , Sep 20, 2005
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        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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