2014/03/31 by Karel Břinda
Computer Science · Mathematics · #cs.DM #math.CO
paper · pdf · doi:10.4204/eptcs.151.9
published as EPTCS 151, 2014, pp. 139-150 · In Proceedings AFL 2014, arXiv:1405.5272
arxiv created 2014/05/22 · arxiv updated 2014/05/23
Several algorithms for similarity search employ seeding techniques to quickly discard very dissimilar regions. In this paper, we study theoretical properties of lossless seeds, i.e., spaced seeds having full sensitivity. We prove that lossless seeds coincide with languages of certain sofic subshifts, hence they can be recognized by finite automata. Moreover, we show that these subshifts are fully given by the number of allowed errors k and the seed margin l. We also show that for a fixed k, optimal seeds must asymptotically satisfy l ~ m^(k/(k+1)).