Design a keypad lock which has three buttons labelledA,BandC. Any of the keys can be pressed at anytime, and if the correct sequence of 5 key presses, namelyBBCBA, is keyed in, then the lock will open.

To solve this problem, do the following.

Let a,b and c be actions representing the actions of pressing buttons A, B and C, respectively; and open and close represent the action of opening, respectively closing, the lock.

Let Sn (for 0 n 5) be state variables, with Sn representing the state in which the last n button presses are the firstnbuttons in the sequence of button presses which opens the lock. Thus, for example, after the sequence of button presses ABCBBC, the process should be in state S3.

(a) Give process definitions for each of the process variables Sn.

b) Draw the labelled transition system for this process.