= {a,b,c}, L = { s : #a (s) = max ( #b (s), #c (s) ) }. Use the pumping theorem to show that L is not a regular language. For example, cab L, but abbc L.

Points to remember when constructing this proof: Start by expressing w in terms of k, where w L, and |w| k.

The goal is to show that for every possible value y, where w = xyz, q(q 0, xyqz L).

For each equivalence class for y, state if you are pumping in or out, and if pumping in how many times.

Do not propose literal values for k, y, or |y|. For example, you cannot assume that |y| is 1, or say something like "let y = ab", or "let k = 1".

Formulas for x and z (the non-pumpable parts of w) are rarely useful. Please do not use them in your proofs.