Question

3. Consider the following “theorem". If L is a regular language then

∀ words w ∈ L where |w| > 1

∃ an expression w = xyz where

(a) ∀i≥0.xyiz∈L

(b) |y| ≥ 1

Explain whether this is a (true) theorem or not

( the question want us to explain why this theorem does not work alone)

Answer #1

The theorem does not works because it does assumes anything about the size of L. if L is finite ,this 'theorem' would not work.

This might look like pumping lemma for regular languages but it is not since the requirement for pumping lemma to work is that L is an infinite Language(otherwise its regular trivially) so that we always find a state in FSA for L, which we visit again and again.

A counterexample for this theorem would be L={a}, the only
choice of y is 'a', but y^{2}=aa does not belong to L

Find a regular expression for the following language
L= {w∈{a,b}*:(na(w)-nb(w)mod)3=1}
please show explanation and steps

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1 Classical Model: The Long Run 1.1 Open Economy Solve for the
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