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Let L3 = {aibcj | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L3. Use the construction of the proof to extend the automaton to one that recognizes L3. Give a path through your extended automaton corresponding to a string in L*3. and show how the argument of the proof splits it into paths through your original automaton.
A.(A+C)=A
Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of
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Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
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We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also
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