Homework 5 Solutions - New Jersey Institute of Technology
NoweachofthevariablesS1 canbeusedtoderiveastringwi ∈A,i.e.,fromthe ithS1,wegetS1 ⇒∗ w i.Thus, S2 ⇒∗ S 1S1 ···S1 ntimes ⇒∗ w 1w2···wn ∈A ∗ since each wi ∈ A.Therefore, we end up with a string in A∗.Toconvince ourselves that the productions applied to the various separate S1 terms do not interfereinundesiredways,weneedonlythinkoftheparsetree.
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