Problem 1 (25%) 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 x and |y. Both the state variables are initialized to 0, and the reaction description is given by: bool in bool out bool x := 0, bool y := 0 if y == True then out := x else out := 0; x := in; y := y. Fig. 1 Synchronous component OddDelay 1) Describe in words the behavior of the component OddDelay.(5%) 2) List a possible execution of the component in the following form if it is supplied with the sequence of inputs 0, 1, 1, 0, 1, 1 for the first six rounds. (10%) in/out (x,y) > (x', y') 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 curre input). (10%)