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given this information of a language I need to determine if the language is regular or not: enter image description here

I thought to Assume by way of contradiction that L6 satisfies the conditions of the pumping lemma. Let p be the pumping constant. Consider the word w = 0^(P-1)1... Clearly w ∈ L6. Thus, by the pumping lemma, there exist x, y, z ∈ Σ^* such that w = xyz, |xy| ≤ p, |y| > 0 where: x = 0^m,
y =0^(p-1-m)1,z = etc, the part that left of t he word. if we take i = 1000 for example we get that xy^1000z not in L because we get the following expression: 000000(00000...001)^1000...z (not in L6), but the solution that provided to similar question shows this: enter image description here

where am I wrong in my attitude to the question?

user1701057
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The language is regular because of the restriction $i_2 < 99$ which makes everything finite. Once you have 99 initial zeroes, it doesn't matter how many more you have. So the pumping lemma isn't going to help. There are a few ten thousand states. Try figuring out what they are.

gnasher729
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  • Thank you, for your fast answer. I see the regular expression and the 10K possibilities, I think I had problem in making assumption as to what thee partition of the word w into xyz looks like, instead of considering all possible options of partition. – user1701057 Apr 09 '23 at 17:20