Minimal dfa.. construction


can we construct a minimal dfa which accepts set of all strings over {a,b,c}, in which occurence of a,b,c must be in geometric progreassion. if yes, then construct the dfa.


no, it is not possible to construct dfa. as we cannot keep track the number of occurance of a, b, c in dfa.
for a,b,c to be in geometric progression, it must satisfy b2=ac. but we cannot keep track of occurance.


Can you explain why we cannot keep track of occurrence. of a,b,c . Can we make an array to store the occurrence of a,b,c and then simultaneously check the occurrences ?