Question

L₁ = {aⁱb^jc^k | i≠j or j≠k or i≠k}.

is'nt this language regular? as this can be equivalent to { aⁱb^jc^k |i,j,k>=0}

because of OR in the question.even if any one is equal then also it will be accepted because of OR.

pls correct me.

and if it is not regular then it is non deterministic PDA??

Comments

language acceptance means u should also reject the strings nt present in the language...so u must see that u shouldnt accept any string where i=j or j=k or i=k...can we do with a finite automata?

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even by simple string checking you can check that both 2 lang are not equal. i.e string "abc", it is accepted by a^ib^jc^k, i,j,k>=0 but not accepted by the provided ang as all 3 OR conditions become false. now we can make CFL for this lang. as S-> S1/S2/S3 where S1 can derive all string where i!=j ,S2can derive all lang where j!=k and same for S3. so it is non deterministic CFL or CFL!!

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yes..i understand that now..thankyou.