In order to optimize the complexity of our algorithm, we want to minimize d, which is the maximum over all rules A → B C of For a fixed binarized grammar, d is always less than p, the tabular parsing complexity, and, hence, the optimal d * over binarizations of an LCFRS is always less than the optimal p * for tabular parsing.
whether any savings can be achieved with our algorithm depends on whether ωd * < p * , or ωd * + 1 < p * in the case of balanced grammars.