Minimal dfa.. construction


#1

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.


#2

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.


#3

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 ?