Unformatted text preview: does not exist such an DFA that recognizes the language of all prime numbers in binary representation. For example, the DFA will accept, 10, 11, 101, 111 and reject 1, 100, 1001. 1. (step 1) Prove that if such a DFA M exists for prime numbers, then there is a inﬁnite sequence of prime numbers a ,a 1 ,...a n ,... with the recursive form that a i +1 = ua i + v for some ﬁxed integer u > 1 and v depending on M. 2. (step 2 (bonus)) Show that for such a sequence, some a i ( i > 0) in a 1 ,a 2 ,..a a must be divisible by a . 1 Zero is a natural number Page 1...
View Full Document
- Spring '09
- Natural number, Prime number, Automata theory