the last paragraph of section discusses strategy for developing solution to new problem by alternating between finding polynomial time solution and proving the problem -complete refine the "algorithm for designing algorithmsfrom section to incorporate identifying and dealing with -complete problems prove that the set of real numbers is uncountable use proof similar to the proof in section that the set of integer functions is uncountable proveusing reduction argument such as given in section that the problem of determining if an arbitrary program will print any output is unsolvable proveusing reduction argument such as given in section that the problem of determining if an arbitrary program executes particular statement within that program is unsolvable proveusing reduction argument such as given in section that the problem of determining if two arbitrary programs halt on exactly the same inputs is unsolvable proveusing reduction argument such as given in section that the problem of determining whether there is some input on which two arbitrary programs will both halt is unsolvable proveusing reduction argument such as given in section that the problem of determining whether an arbitrary program halts on all inputs is unsolvable proveusing reduction argument such as given in section that the problem of determining whether an arbitrary program computes specified function is unsolvable consider program named comp that takes two strings as input it returns true if the strings are the same it returns false if the strings are different why doesn' the argument that we used to prove that program to solve the halting problem does not exist work to prove that comp does not exist projects implement vertex coverthat isgiven graph and integer kanswer the question of whether or not there is vertex cover of size or less begin by using brute-force algorithm that checks all possible sets of vertices of size to find an acceptable vertex coverand measure the running time on number of input graphs then try to reduce the running time through the use of any heuristics you can think of nexttry to find approximate solutions to