$]$ You are working as an applied scientists at IBM Research. You are tasked with designing an anomaly detection system for a complex network protocol used in secure communications. The protocol involves a series of messages between a client and a server, represented as sequences of events over an alphabet defined as: C: Client sends a connection request H: Server sends a handshake message S: Secure key exchange occurs D: Client sends data A: Server sends an acknowledgment F: Client sends a finish request to terminate the session T: Server sends a termination confirmation E: An error occurs $($could be on client or server side$)$ R: Retransmission of the last message $($either by client or server$)$ Provide Regular Expression for the following: a$.$ Connection Establishment: $[10$pts$]$ i$.$ The client initiates a connection by sending a connection request $($C$),$ possibly followed by any number of errors $($E$).$ ii$.$ The server responds with a handshake $($H$).$ If an error $($E$)$ occurs after the handshake, the server must retransmit the handshake $($H$).$ This can happen any number of times. iii. After a successful handshake, a secure key exchange $($S$)$ occurs exactly once, possibly preceded and$/$or followed by errors $($E$).$ If any error occurs after the key exchange and before data transmission begins, the client must restart the connection process by sending another connection request $($C$),$ and the process from step $1$ repeats.