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Of the 40th Symposium of Foundations of Computer Science (FOCS99), pages 512–522, 1999. 11. J. Gramm, J. Guo, and R. Niedermeier. Pattern matching for arc-annotated sequences. In Proc. of the 22nd Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS02), volume 2556 of LNCS, pages 182– 193, 2002. 12. J. Guo. Exact algorithms for the longest common subsequence problem for arcannotated sequences. Master’s Thesis, Universitat Tubingen, Fed. Rep. of Germany, 2002.

By Lemma 3, any corresponding alignment of (S, P ) and (T, Q) is canonical. Therefore, Txsm is matched with either Sxsm A or A Sxsm . Consequently, for any 1 ≤ m ≤ n, we define an assignment AS of the variables of I as follows: – if Txsm is matched with Sxsm A then xm = F alse, – otherwise, xm = T rue. Now, let us prove that for any 1 ≤ i ≤ q the clause ci is satisfied by AS. e. c1 ). c1 is defined by three literals (say xi , xj and xk ). Since, c1 is equal to the disjunction of variables built with xi , xj and xk , c1 can have eight different forms, because each literal can appear in either What Makes the Arc-Preserving Subsequence Problem Hard?

This slight error can probably be ascribed to our “hit-andextend” searching strategy to resolve the difficulty arising from the complex structure and the relatively much larger size of tmRNA genes; positional errors may occur during different searching stages and accumulate to a significant value. Our experiment on the Profiling and Searching for RNA Pseudoknot Structures in Genomes 43 DNA genomes also demonstrates that, for each genome, it is very likely there is only one tmRNA gene in it, since our program found only one significant hit.

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