Take the 2-minute tour ×
Theoretical Computer Science Stack Exchange is a question and answer site for theoretical computer scientists and researchers in related fields. It's 100% free, no registration required.

Input: Any number $n \in \mathbb{Z}^+$ that can be represented in the form of $n = 2^a + b,\ |b|= c $. output: YES if $n$ is prime , else NO .

Now, length of binary input is $\log(a) + O(1)$ which otherwise would be order $a$. What would be the complexity of such problem? If we use AKS algorithm in straight forward way we would not get polynomial time algorithm, I think. Can we define new problems by tweaking the standard problems in P to make them harder in this way i.e. by restricting the input in certain way.

share|improve this question
1  
The succinct version of problems are exponentially harder (e.g. Succinct-SAT is NExpTime-complete). Yours is a restricted case of succinct version of Prime. –  Kaveh Dec 30 '12 at 6:14
    
Thanks, I was not aware that succinct version of problems is already well explored area. –  DurgaDatta Dec 30 '12 at 6:26
    
You are welcome. ps: You may want to have a look at Russell Impagliazzo's answer to the padding question. –  Kaveh Dec 30 '12 at 6:28
    
@Kaveh make this an answer ? –  Suresh Venkat Jan 2 '13 at 16:50
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.