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

Fig. $1$ Synchronous component OddDelay

$1)$ Describe in words the behavior of the component OddDelay. $(5\backslash \%)$

$2)$ List a possible execution of the component in the following form if it is supplied with the sequence of inputs $\backslash (0,1,1,0,1,1\backslash )$ for the first six rounds. $(\backslash (10\backslash \%\backslash ))$

$\backslash [$

$($x$,$ y$)\backslash$xrightarrow$\{\backslash$text $\{$ in$/$out $\}\}\backslash$left$($x$^\{\backslash$prime$\},$ y$^\{\backslash$prime$\}\backslash$right$)$

$\backslash ]$

$3)$ Is the component finite$-$state? Draw the state machine of the component $($label the input and output on each state transition in the form of input$/$output $($i$.$e$.,$ the output is determined by both current state and current input$).(10\backslash \%)$