Please solve Exercise 2.1 using the knowledge of example 1

oktkotkkokk ckixxt ttokxxxttoxxxxioktokktokkicookxkixxk*cikkcxkxxttokc Example 1 Delay bool in | bool x :=0 bool out Figure 2.1: Reactive Component Delay Formally, an erecution of a synchronous reactive component C of length k, where k 0, consists of a finite sequence of the form h/ 8081 i3/ 83 8k-l 8k, Where: 1. for 0 sjs k, each s, is a state of C, and for 1 sjS k, each ij is an input of C, and each Oj is an output of C; 2. so is an initial state of C; and 3. for 1 sjsk, s,-1 3sz is a reaction C For instance, one possible execution of the Delay component of length 6 is: Exercise 2.1: Consider a modified version of the Delay component, called OddDelay, that has a Boolean input variable , 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; Describe in words the behavior of the component OddDelay. List a possible exe- cution of the component if it is supplied with the sequence of inputs 0,1,1,0,1, 1 for the first six rounds. oktkotkkokk ckixxt ttokxxxttoxxxxioktokktokkicookxkixxk*cikkcxkxxttokc Example 1 Delay bool in | bool x :=0 bool out Figure 2.1: Reactive Component Delay Formally, an erecution of a synchronous reactive component C of length k, where k 0, consists of a finite sequence of the form h/ 8081 i3/ 83 8k-l 8k, Where: 1. for 0 sjs k, each s, is a state of C, and for 1 sjS k, each ij is an input of C, and each Oj is an output of C; 2. so is an initial state of C; and 3. for 1 sjsk, s,-1 3sz is a reaction C For instance, one possible execution of the Delay component of length 6 is: Exercise 2.1: Consider a modified version of the Delay component, called OddDelay, that has a Boolean input variable , 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; Describe in words the behavior of the component OddDelay. List a possible exe- cution of the component if it is supplied with the sequence of inputs 0,1,1,0,1, 1 for the first six rounds