I was interested to find out how you center yourself and clear your

thoughts before writing. I’ve had a tough time clearing my mind in getting my ideas out there.

I do enjoy writing but it just seems like the first 10 to 15 minutes tend to be wasted simply just trying to figure

out how to begin. Any suggestions or tips? Kudos! ]]>

It’s awesome to come across a blog every once in a while that

isn’t the same old rehashed material. Excellent read!

I’ve bookmarked your site and I’m including your RSS feeds to my Google account.

I show a solution to that problem as follows:

Given a number x and a set S of n positive integers, MINIMUM is the problem of deciding whether x is the minimum of S. We can easily obtain an upper bound of n comparisons: find the minimum in the set and check whether the result is equal to x. Is this the best we can do? Yes, since we can obtain a lower bound of (n – 1) comparisons for the problem of determining the minimum and another obligatory comparison for checking whether that minimum is equal to x. A representation of a set S with n positive integers is a Boolean circuit C, such that C accepts the binary representation of a bit integer i if and only if i is in S. Given a positive integer x and a Boolean circuit C, we define SUCCINCT-MINIMUM as the problem of deciding whether x is the minimum bit integer which accepts C as input. For certain kind of SUCCINCT-MINIMUM instances, the input (x, C) is exponentially more succinct than the cardinality of the set S that represents C. Since we prove that SUCCINCT-MINIMUM is at least as hard as MINIMUM in order to the cardinality of S, then we could not decide every instance of SUCCINCT-MINIMUM in polynomial time. If some instance (x, C) is not in SUCCINCT-MINIMUM, then it would exist a positive integer y such that y < x and C accepts the bit integer y. Since we can evaluate whether C accepts the bit integer y in polynomial time and we have that y is polynomially bounded by x, then we can confirm SUCCINCT-MINIMUM is in coNP. If any single coNP problem cannot be solved in polynomial time, then P is not equal to coNP. Certainly, P = NP implies P = coNP because P is closed under complement, and therefore, we can conclude P is not equal to NP.

You could read the details in the link below…

]]>It was funny. Keeep oon posting! ]]>

reasonably. Climb all the way to the top, picking up a handful of useful items along the way if you wish.

) into an intense, and gripping war of the new millennia. ]]>