4. Let be an arbitrary alphabet. For every w *, if w = E,...

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4. Let Σ be an arbitrary alphabet. For every w € *, if w = E, {x |cx if w = xc for some x € Σ* and c e Σ. For every language L CE*, we define p(w) =. R(L)= {xe E*: x = p(y) for some y = L}. Prove that if L is a regular language, then so is R(L). More specifically, you must show the construction of a DFA for R(L) based on a DFA for L. Present your DFA by giving its formal definition, NOT diagrams. 4. Let Σ be an arbitrary alphabet. For every w E E*, if w = E, {x |cx if w = xc for some x € Σ* and c e Σ. p(w) =. For every language L CE*, we define R(L) = (x e E*: x = p(y) for some y L}. Prove that if L is a regular language, then so is R(L). More specifically, you must show the construction of a DFA for R(L) based on a DFA for L. Present your DFA by giving its formal definition, NOT diagrams. 4. Let Σ be an arbitrary alphabet. For every w € *, if w = E, {x |cx if w = xc for some x € Σ* and c e Σ. For every language L CE*, we define p(w) =. R(L)= {xe E*: x = p(y) for some y = L}. Prove that if L is a regular language, then so is R(L). More specifically, you must show the construction of a DFA for R(L) based on a DFA for L. Present your DFA by giving its formal definition, NOT diagrams. 4. Let Σ be an arbitrary alphabet. For every w E E*, if w = E, {x |cx if w = xc for some x € Σ* and c e Σ. p(w) =. For every language L CE*, we define R(L) = (x e E*: x = p(y) for some y L}. Prove that if L is a regular language, then so is R(L). More specifically, you must show the construction of a DFA for R(L) based on a DFA for L. Present your DFA by giving its formal definition, NOT diagrams.