n problem2.jff, build a deterministic finite-state machine that accepts all bit strings in which the number of 0s is either a multiple of two, a multiple of three, or a multiple of both two and three, and that rejects all other bit strings. The number of 1s does not matter.

This problem requires at least six states. You may use more states if necessary (theres no penalty for doing so), but if you have time, try to get as close to the minimum as possible!

Here are three examples of strings that should be accepted:

111 # zero 0s -- and zero is a multiple of both 2 and 3! 0111011111110 # three 0s 11110100000111 # six 0s 

Here are three strings that should be rejected:

1011 0010010 1000100001