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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.
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Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi
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