Homework Assignment 1 Note: Students should start working on homework as early as possible. Please work by yourself and submit your solution as one pdf file to Problem 1 (40 points): 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. Recall that Delay is: bool in bool x 0 bool out out := x - in