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I have a language $L = \{ a^i b^j c^k \mid i \geq 1 \land j \geq 1 \land k \geq 1 \land (i \neq j \lor j \neq k) \}$ and how to check if it is regular language? I tried using pumping lemma for regular languages, but I have no idea which word I should choose.

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Hint : this does not seem to be a regular language since a finite state automata would have to keep count of the number of a's he saw to verify it is different from the number of b's (similarly with the c's)

Using the pumping lemma seems difficult since we would like to get to a word thats not in the language and such words are constrained with i=j=k that is difficult to get to.

But, show that the complement language is not regular, take a word of the above form with i=j=k and pump it so that the part of the word that is being pumped have only a and b or b and c in it so pumping will make j bigger than one of a or c

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