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Manupulative codewords - Hofstadter's MIU system
This system of codewords have only stings of letters formed from the alphabets, M, I, U with MI as one of the codewords. You can form other codewords in the system by the following four rules :
x in the below lines can be any string of letters from M, I, U that makes a codeword in each of the rules.
1. If xI is a codeword, then xIU is also a codeword.
2. If Mx is a codeword, Mxx is also a codeword.
3. In any codeword, III can be replaced by U.
4. In any codeword, UU can be omitted.
Questions : Show that MUII is a codeword. Is MU a codeword?
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1 comment:
Xixu and I say: apply rule #2 3 times, then #3 to change the first 3 I's to a U, then #1 to add a U at the end, then #3 to change the last 3 I's to a U, and finally #4 to get rid of the UU. Looks like:
MI->MII->MIIII->MIIIIIIII->MUIIIII->MUIIIIIU->MUIIUU->MUII
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