We design a sublinear time parallel algorithm for the computation of the general dynamic programming recurrences. Its total work matches the work of the best known sequential algorithm. It is the first optimal sublinear parallel time algorithm for this problem. Using similar methods we construct also sublinear time parallel algorithms for the recognition of linear, unambiguous and deterministic cfl's. Their total works are O(T(n)αlog(n)), for arbitrarily small constant α<1, where T(n) is the work of the best known sequential algorithm for the problem. This reduces substantially the gap between the total work of sublinear time parallel algorithms and that of the best known sequential algorithms.