Symbolic dynamics provides a wealth of analytical tools for studying infinite strings of symbols that arise from continuous-time dynamical systems. Surprisingly, few of these techniques have been adapted for use with finite strings of symbols. In this talk, I will detail the adaptation of two such tools: topological entropy and pressure. Fortuitously, these tools are well adapted to studying DNA sequences. Results will be given on the efficacy of applying such techniques to a variety of genomic analysis problems (including intron/exon classification and gene density estimation).