Assessing the significance of sets of words

Various criteria have been defined to evaluate the significance of sets of words, the computation of them often being difficult. We provide explicit expressions for the waiting time in such a context. In order to assess the significance of a cluster of potential binding sites, we extend them to the co-occurrence problem. We point out that these criteria values depend on a few fundamental parameters. We provide efficient algorithms to compute them, that rely on a combinatorial interpretation of the formulae. We show that our results axe very tight in the so-called twilight zone and improve on previous rough approximations. One assumes that the text is generated according to a Markov stationary process. These results axe developed for an extended model of consensus.