1.(Dataflow) The intraprocedural must-be-modified problem is a backward data flow problem solvable by fixed point iteration. A variable is in the must-be-modified set on exit of a cfg node, if it is modified unconditionally on all paths from this node to program exit.

a. Define the data flow framework for this problem (i.e, give the lattice, its partial order operator, its meet and the functions describing how the code at each node affects the lattice elements. (Hint: define the base lattice and then build the cross product lattice from it.)

b. Are the functions for this problem distributive or monotone? Explain briefly.