Minimum Pumping Length

Question

What is the minimum pumping length of following language L=10 (11* 0)* 0

I have read a statement like this

s = xyz = 10100 where x=10,y=10 and z=0 such that xyiz∈L (that is 10(1∊0)*0 ) Well it looks Minimum Pumping length is 5 , But it is not, We can repeat y any time (or it should be) and y≠≠ ∊ that mean we cannot use 3 or less length string from L for pumping , So y can be 10 (minimum) so minimum string S we using for pumping is 10100 of length 5, but length 4 string can not generated from the given language (that's not our fault). So we can say we use 4 or more length string s for pumping that belongs to L. Therefore pumping length is 4

But , I am confused with this . y=10 , SO what made the author say pumping length of three or less possible ? it has to be two or less. Don't it ? if pumping length of 4 is possible it has to be accepted by Language L . Doesn't it ? Please help me find the minimum puping length of this question

Answer 1

The minimum pumping length is a minimum constant C such that any string of the language with length greater or equal C can be pumped (as far as i remember). The author of the citation said that minimum length of existing string that can be pumped is 5 for the regular expression but there are no strings with length 4 in the language so it is safe to say that minimum pumping length is 4 because it appropriate for the definition.