 The exact values of the Chvátal–Sankoff constants remain unknown, but rigorous upper and lower bounds have been proven.Because formula_1 is a supremum of the values formula_6 which each depend only on a finite probability distribution, one way to prove rigorous lower bounds on formula_1 would be to compute the exact values of formula_6; however, this method scales exponentially in "n", so it can only be implemented for small values of "n", leading to weak lower bound.In his Ph.D. thesis, Vlado Dančík pioneered an alternative approach in which a deterministic finite automaton is used to read symbols from two input strings and produce a (long but not optimal) common subsequence of this inputs.