We present improvements to two techniques to find lower and upper
bounds for the expected length of longest common subsequences and
forests of two random sequences of the same length, over a fixed
size, uniformly distributed alphabet. We emphasize the power of the
methods used, which are Markov chains and Kolmogorov complexity. As a
corollary, we obtain some new lower and upper bounds for the problems
addressed as well as some new exact results for short sequences.
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