Give reductions from the hello-world problem to each of the problems below. Give informal descriptions for your program transformations. The hello-world problem is: Given a program and an input, does the program print hello-world as the first 11 characters that it prints? It is easy to see that this modified hello-world problem is also undecidable by the same proof by contradiction we discussed in the class.

a. Given a program and an input, does the program ever produce any output?

b. Given a program and an input, does the program eventually halt?