▁returns ▁no ▁meaning ful ▁result ▁or ▁a ▁match ▁occurs . ▁These ▁tables ▁will ▁be ▁designated ▁ ▁and ▁ ▁respectively . ▁Their ▁definitions ▁are ▁as ▁follows : ▁ ▁For ▁each ▁, ▁ ▁is ▁the ▁largest ▁position ▁less ▁than ▁ ▁such ▁that ▁string ▁ ▁matches ▁a ▁suffix ▁of ▁ ▁and ▁such ▁that ▁the ▁character ▁preceding ▁that ▁suffix ▁is ▁not ▁equal ▁to ▁. ▁ ▁is ▁defined ▁to ▁be ▁zero ▁if ▁there ▁is ▁no ▁position ▁satisfying ▁the ▁condition . ▁ ▁Let ▁ ▁denote ▁the ▁length ▁of ▁the ▁largest ▁suffix ▁of ▁ ▁that ▁is ▁also ▁a ▁prefix ▁of ▁, ▁if ▁one ▁exists . ▁If ▁none ▁exists , ▁let ▁ ▁be ▁zero . ▁ ▁Both ▁of ▁these ▁tables ▁are ▁construct ible ▁in ▁ ▁time ▁and ▁use ▁ ▁space . ▁The ▁alignment ▁shift ▁for ▁index ▁ ▁in ▁ ▁is ▁given ▁by ▁ ▁or ▁. ▁ ▁should ▁only ▁be ▁used ▁if ▁ ▁is ▁zero ▁or ▁a ▁match ▁has ▁been ▁found . ▁ ▁The ▁Gal il ▁rule ▁A ▁simple ▁but ▁important ▁optimization ▁of ▁Bo yer – Mo ore ▁was ▁put ▁forth ▁by ▁Gal il ▁in ▁ 1 9 7 9 . ▁As ▁opposed ▁to ▁sh ifting , ▁the ▁Gal il ▁rule ▁de als ▁with ▁speed ing ▁up ▁the ▁actual ▁compar isons ▁done ▁at ▁each ▁alignment ▁by ▁ski pping ▁sections ▁that ▁are ▁known ▁to ▁match . ▁Suppose ▁that ▁at ▁an ▁alignment ▁, ▁ ▁is ▁compared ▁with ▁ ▁down ▁to ▁character ▁ ▁of ▁. ▁Then ▁if ▁ ▁is ▁shift ed ▁to ▁ ▁such ▁that ▁its ▁left ▁end ▁is ▁between ▁ ▁and ▁, ▁in ▁the