Discuss the relationship between bounded summation and the concept of a finite upper bound.

4. Use the formal definitions of (•) and O( • ) to show that: 15n² + 12n + 18 is in (n) and in O(n²). 5nlogn + 8n + 10 is in (nlogn)

Reduce the following lambda calculus terms to the normal form. Show all intermediate steps, with one beta reduction at a time. In the reduction, if necessary, assume that you are supplied with extra rules that allow you to rehice the additLion of two natural mumbers into the corresponding result. (Az. 2) (Ny. y y) (\x. z a).

In regards to P/NP can you explain what exactly is the concept of reducibility?

2. Consider the language DOUBLE-SAT, all of the boolean expressions with at least two satisfying assignments. (a) What would a possible DOULBE-SAT solution look like for an expression? (b) Is DOUBLE-SAT in NP?