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 $1,0,0,$

$1,0,1,1,1,0,1$ 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.

Recall that Delay is: