Question: 4. (30 points) Let L be any language and let L - be the set of all the first halves of strings in L, i.e.

4. (30 points) Let L be any language and let L

4. (30 points) Let L be any language and let L - be the set of all the first halves of strings in L, i.e. L2- = {z | Jy S* such that [2] = ly| and xy L}. As an example, if L = {happy, computation, automata, finite}, then L4- = {auto, fin}. Show that if L is a regular language then 17- is regular. Hint: Think about the way we implemented two machines in "parallel" by using the Cartesian product. That idea may be useful for this

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