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In this paper, we develop new algorithms for the basic RNA folding problem.Given an RNA sequence that contains $n$ nucleotides, the goal of the problem isto compute a pseudoknot-free secondary structure that maximizes the number ofbase pairs in the sequence. We show that there exists a dynamic programmingalgorithm that can solve the problem in time $O(\frac{n^{3}}{\log_{2}{n}})$while using only $O(\frac{n^{2}}{\log_{2}{n}})$ memory space. In addition, weshow that the time complexity of this algorithm can be further improved to$O(\frac{n^{3}}{\log_{2}^{2}{n}})$ at the expense of a slightly increased spacecomplexity. To the best of our knowledge, this is the first algorithm that cansolve the problem with traditional dynamic programming techniques in time$O(\frac{n^{3}}{\log_{2}^{2}{n}})$. In addition, our results improve the bestknown upper bound of the space complexity for efficiently solving both thisproblem and the context-free language recognition problem.

Time and Space Efficient Algorithms for RNA Folding with the Four-Russians Technique