In Kellis et al. (2003), we reported the genome sequences of S. paradoxus, S. mikatae, and S. bayanus and compared these three yeast species to their close relative, S. cerevisiae. Genomewide comparative analysis allowed the identification of functionally important sequences, both coding and noncoding. In this companion paper we describe the mathematical and algorithmic results underpinning the analysis of these genomes. (1) We present methods for the automatic determination of genome correspondence. The algorithms enabled the automatic identification of orthologs for more than 90% of genes and intergenic regions across the four species despite the large number of duplicated genes in the yeast genome. The remaining ambiguities in the gene correspondence revealed recent gene family expansions in regions of rapid genomic change. (2) We present methods for the identification of protein-coding genes based on their patterns of nucleotide conservation across related species. We observed the pressure to conserve the reading frame of functional proteins and developed a test for gene identification with high sensitivity and specificity. We used this test to revisit the genome of S. cerevisiae, reducing the overall gene count by 500 genes (10% of previously annotated genes) and refining the gene structure of hundreds of genes. (3) We present novel methods for the systematic de novo identification of regulatory motifs. The methods do not rely on previous knowledge of gene function and in that way differ from the current literature on computational motif discovery. Based on genomewide conservation patterns of known motifs, we developed three conservation criteria that we used to discover novel motifs. We used an enumeration approach to select strongly conserved motif cores, which we extended and collapsed into a small number of candidate regulatory motifs. These include most previously known regulatory motifs as well as several noteworthy novel motifs. The majority of discovered motifs are enriched in functionally related genes, allowing us to infer a candidate function for novel motifs. Our results demonstrate the power of comparative genomics to further our understanding of any species. Our methods are validated by the extensive experimental knowledge in yeast and will be invaluable in the study of complex genomes like that of the human.