Question: 3. Design a keypad lock which has three buttons labelled A, B and C. Any of the keys can be pressed at any time,

3. Design a keypad lock which has three buttons labelled A, B and C. Any of the keys can be pressed at any

3. Design a keypad lock which has three buttons labelled A, B and C. Any of the keys can be pressed at any time, and if the correct sequence of 5 key presses, namely BBCBA, 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 S (for 0 < n 5) be state variables, with S representing the state in which the last n button presses are the first n buttons 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. [10 marks]

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