Answer Happy

Design a keypad lock which has three buttons, labelled A, B and C respectively. Any of these three keys can be pressed at any time; and if the correct sequence of three key presses, namely BCA, is keyed in, then the lock will pop open. For example, the sequence of button presses ABCBCA will cause the lock to pop open, since it ends with ВСА. 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, respectively, represent the actions of opening and closing the lock. • Let So, S1, S2 and S3 be state variables, with Sn representing the state in which the last n buttons pressed are the first n buttons in the sequence of button presses which opens the lock. Thus, for example, after the sequence of button presses ACBBC, the process should be in state S2 as the last two button presses are BC, i.e., the first two button presses of the correct sequence BCA. (a) Give process definitions for each of the process variables Sn. As a start, def So a.S. + b.S; + c.So That is, • if the B button is pressed, then move to the state S, representing the fact that the first correct button has been pressed; • if any other button is pressed, then stay in the state So representing the fact that no correct button has been pressed. Remember to include the action open from state S3, as well as the action close from the resulting state. [5 marks) (b) Draw the labelled transition system for this process. [5 marks]