the set of all strings such that the no of zero’s is divisible by 5 and the no of 1’s is divisible by 3. Draw an NFA for the same language, using at most nine states. After some trial and error, I found that the lowest number that works is 300, which is 5xx60. I was given a task to find RE and NFA for a word that is divisible by 5. 8 => 1000 (divisible) 16 => 10000 (divisible) 32 => 100000 (divisible) 33 => 100001 (not divisible) Hence, we observe that for numbers to be divisible by 4, the last two bits should be 0, because if both of them or either of them becomes 1, the sum of those two bits in decimal wouldn’t be divisible by 4. Rule: A number is divisible by 6 if it is even and if the sum of its digits is divisible by 3.

Based on the DFA proposed by the author, a ridiculously short regex can be generated by simplifying the routes a binary string can take through the DFA. The quick and dirty tip to check for divisibility by 3 is to see if the sum of all the digits in the number is divisible by 3. The accepting states are $\{q_0,q_2,q_3,q_4\}$, since a number is even or divisible by 3 iff its residue modulo 6 is one of 0,2,3,4. {1,2} ∅ a {1,2,3} b a Now we determine where the b-edge from DFA state {1,2,3} goes to. n³ - n = n (n² - 1) = n (n - 1) (n + 1) If n = 3p, then n is divisible by 3. When the number is divisible by 2, then it will go from state q1 to q0 or if it was initially in q0 then it will accept it. DFA that accepts all binary strings divisible by 5. For any positive integer n prove that n cube minus n is divisible by 6 when any number is divided by 3 the remainder is 0, 1, 2 now according to question hence, n = 3p or 3p + 1 or 3p + 2, here p is some integer. This set of Automata Theory Multiple Choice Questions & Answers (MCQs) focuses on “Finite Automata”. 3. Justify your Answer. Eg: 011 => 3 (not divisible by 4) Draw an NFA for the same language, using at most nine states. How to Tell if a Number is Divisible by 3. What language is accepted by the following DFA?

Statement 1: Null string is accepted in Moore Machine. i.e. 1. Draw a DFA for the set of strings over the alphabet \a\ whose length is divisible by 3 or 5 (or both). So there are 8 states (4*2) which include 3 final states.
The quick and dirty tip to check for divisibility by 3 is to see if the sum of all the digits in the number is divisible by 3.

19. Define the language of NFA. 1.2a in the text; 1.2b in the text. Statement 2: There are more than 5-Tuples in the definition of Moore Machine. If so, the number itself must also be divisible by 3. Convert the NFA in 2f into a DFA. Combine both the above automata to construct DFA that accepts all the strings with the total number of ‘a’ is an odd & total number of b’s is not divisible by 3.

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