1. Consider a set of (nested) list structures described by a context-free grammar with the fol- lowing productions: S (A) A B , A, B Find a pushdown automaton which accepts only those (correct) list structures which con- tain not more then three elements at each level; for example, "(a, (a,a,a), ((a),a))" and "C(a),a, ((a,a),a))" should be accepted but "((a),a, (a,a),a)" should not Hint: Use consecutive elements of the stack as counters of the number of elements on the corresponding levels of the analyzed list structure