Clarification on finding a break point
I watched the lectures and went through the book, but I had some questions with my understanding after working on the homework exercises. I seem to be lost in somewhat of a circular argument. My understanding is that if k is a breakpoint, then m_H(n) < 2^k. I can find B(n, k), which if k is a breakpoint for H, m_H(n) < B(n, k). I think I follow the logic of the proofs and bounding, where if we can prove that B(n, k) is bounded by a polynomial, then clearly values smaller than B(n, k) are also bounded by polynomials. What I thought I had seen/heard when I was reading the text book and watching the lectures was a formula for discovering m_H(n) without using pure inspection, but now I can't seem to find it. Is there a formula for discovering m_H(n), or is it found only by inspection? If so, can someone point me to where this is discussed?
