Context Free Languages

Question

{${a^{i}b^{j}c^{k}| (i\leq j)or(j\leq i),j=k}$} is CFL?

Answer 1

yes its cfl, when you compare i and j only two cases happen either i is less than or equal to j or j is less than equal to i. So we don't need to check this condition. Remaining is j=k. So you can write above language as

  $L = \left \{a^{i}b^{n}c^{n} \right \}$, which is certainly a CFL.

Comments

and If (j<i or i<j )and j=k then it is not a CFL, correct @stblue?

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yes, in previous case we avoided comparison between i and j, but now we do have to compare i and j as well, so now we have to first compare between a and b, then we have to compare between b and c, which we certainly can't do in CFL.
L = { $a^{i}b^{j}c^{k} |$ i != j and j=k }
This language will be CSL.