Wright State University Inductive Invariant of the Transition System Questions

Problem 1 (40 points): Given two natural numbers ?? and ??, consider the program Mult thatmultiplies the input numbers using two state variables ?? and ??, of type nat, as shown in the figurebelow.

Problem 2 (60 points):For this question, we will try out the NuXmu model checker tool with anexample of the program Mult in Problem 1.fo

Problem 3 (20 bonus points): Recall the synchronous design of a cruise controller system fromsection 2.4.2 in Alur’s book and Problem 2 in Homework Assignment 1. Consider the followingrequirement: when the cruise-controller is “on,” assuming the driver does not issue any furtherinput events, eventually the speed becomes equal to the desired cruising speed and stays equal.Express this requirement in LTL using the variables on, speed, cruiseSpeed, cruise, inc, and dec