We propose in this part to apply our results to the computation of exact p-values for local score. We first recall the definition of the local score of one sequence (section 3.1) and design a FMCI allowing to compute p-value in the particular case of an integer and i.i.d. score (section 3.2). We explain in sections 3.5 and 3.6 how to relax these two restrictive assumptions to consider rational or Markovian scores. The main result of this part is given in section 3.4 where we propose an algorithm improving the simple application of the general ones by using a specific asymptotic behaviour presented in section 3.3. As numerical application, we propose finally in section 3.7 to find significant hydrophobic segments in the Swissprot database using the Kyte-Doolittle hydrophobic scale. Our exact results are compared to the classical Gumble asymptotic approximations and discussed both in terms of numerical performance and reliability.