""
  "0"
  "00" "11"
  "000" "101" 
  "0000" "1111" "1001" "1111"
  "00000" "10101"
[download]

I regret to inform you that 101 is not matched, though 110 and 011 are. (abell's solution is correct.)

I'm a bit gratified that people seem to be having a fairly difficult time with this (must be the (01*0)* group in the middle of the right-hand alternative; I think people tend to see the 01 as both bound by the *, rather than just the 1): means it's a useful example.

Oh, and the completeness proof for this regex matching multiples of three is fairly straightforward, once you have a minimal DFA for matching this regex. (In short: your minimal DFA has three states, each corresponding to a modulus of 3. 0 is the only accepting state, and you can prove by contradiction that all multiples of 3 end up in the 0 state.) Maybe I'll write it up when my profs stop assigning me papers. %-)

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