ed ▁and ▁solved ▁Tra ht man ' s ▁solution ▁to ▁the ▁road ▁color ing ▁problem ▁was ▁accepted ▁in ▁ 2 0 0 7 ▁and ▁published ▁in ▁ 2 0 0 9 ▁by ▁the ▁Israel ▁Journal ▁of ▁Mathemat ics . ▁The ▁problem ▁arose ▁in ▁the ▁sub field ▁of ▁symbol ic ▁dynamics , ▁an ▁abstract ▁part ▁of ▁the ▁field ▁of ▁dynam ical ▁systems . ▁The ▁road ▁color ing ▁problem ▁was ▁raised ▁by ▁R . ▁L . ▁Ad ler ▁and ▁L . ▁W . ▁Good w yn ▁from ▁the ▁United ▁States , ▁and ▁the ▁Isra eli ▁math ematic ian ▁B . ▁We iss . ▁The ▁proof ▁used ▁results ▁from ▁earlier ▁work . ▁ ▁Č ern ý ▁conject ure ▁The ▁problem ▁of ▁estim ating ▁the ▁length ▁of ▁synchron izing ▁word ▁has ▁a ▁long ▁history ▁and ▁was ▁pos ed ▁independently ▁by ▁several ▁authors , ▁but ▁it ▁is ▁commonly ▁known ▁as ▁the ▁Č ern ý ▁conject ure . ▁In ▁ 1 9 6 4 ▁Jan ▁Č ern ý ▁conject ured ▁that ▁ ▁is ▁the ▁upper ▁bound ▁for ▁the ▁length ▁of ▁the ▁short est ▁synchron izing ▁word ▁for ▁any ▁n - state ▁complete ▁D FA ▁( a ▁D FA ▁with ▁complete ▁state ▁transition ▁graph ). ▁If ▁this ▁is ▁true , ▁it ▁would ▁be ▁tight : ▁in ▁his ▁ 1 9 6 4 ▁paper , ▁Č ern ý ▁exhib ited ▁a ▁class ▁of ▁autom ata ▁( index ed ▁by ▁the ▁number ▁n ▁of ▁states ) ▁for ▁which ▁the ▁short est ▁reset ▁words ▁have ▁this ▁length . ▁In ▁ 2 0 1