Assume that each of the expressions in the following table has processing time T(n) to solve a problem of size n. Identify the dominant term(s) having the growing increase in n and specify the Big-Oh complexity.   Expression Dominant term(s) Big-Oh A.1 8 + 0.081n2 + 0.040n     A.2 100 + n log2 n     A.3 100n + 0.081 log3 n + n3     A.4 0.081 log4 n + 81n

Given an integer say 45, to find the sum of 45 with 8 in binary form (see the figure below), we can use the TM designed in slides 79-90 of the notes "Turing Machines and Equivalent Models I" twice to find the result. A more effective way is to design a TM to do the addition with 8 directly. 1000 101101 A + = ? Such a TM can be designed by extending the TM designed in slides 79-90 of the notes "Turing Machines and Equivalent Models I". The TM has 14 instructions and 6 states: 0, 1, 2, 3, 4, and halt. Six instructions of such a TM have been given in the first and the second tables below. Fill out the remaining blanks in the first and the second tables and also blanks in the third table to show the remaining instructions of the TM (you have to use your own text boxes here)

Define sequences a1, a2, a3,a4,..… by the following explicit formula:      ak = k+ 1 / k+ 3       Compute the first four terms   a1= a2= a3= a4=