Answer the following FIVE questions. Submit your responses in a PDF file. 1. In formal writing, describe Lamport's algorithm for distributed mutual exclusion. 2. Prove that this algorithm satisfies ME1, ME2, and ME3. 3. Prove that this algorithm guarantees a starvation free solution. 4. Modify or enhance Lamports mutual exclusion algorithm for the following system: Each pair of PE has only one communication path (consisting of a sequence of FIFO channels) with a fixed propagation delay. Different paths may have different delays and the delay of each path is not known when the system starts. Only physical clocks are used and all of them are accurate and are synchronized initially. Consider various modifications and enhancements and discuss their pros and cons. 5. Suppose the request sets of a six-process system are the following: R1: {P1,P2,P3,P4,P5,P6} R2:{P1,P3} R3:{P2,P3} R4:{P1,P2} R5:{P2,P3} R6:{P1,P3} What is the potential problem for the above arrangement?