Understanding the Behavior of OddDelay

CPS 592 Cyber Physical Systems

Task:

Consider a modified version of the Delay component, called OddDelay, that has a Boolean input variable in, a Boolean output variable out, and two Boolean state variables x and y. Both the state variables are initialized to 0, and the reaction description is given by:

if y then out := x else out := 0;

x := in;

y := ¬y.

a. Describe in words the behavior of the component OddDelay. (Hint: what is the output at odd and even rounds?)

b. List a possible execution of the component if it is supplied with the sequence of inputs 0, 1, 1,

0, 1, 1, 1, 0, 0, 1 for the first tenth rounds.

c. Describe the component OddDelay as an extended-state machine with two modes. The mode

of the state machine should capture the value of the state variable y, while the state variable x should be updated using assignments in the mode-switches.

d. Is the OddDelay component finite-state? Draw the corresponding Mealy machine.

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