Final answer:
ME1, ME2, and ME3 are proven to be satisfied in different distributed systems using formal proofs and, if necessary, proof by contradiction.
Step-by-step explanation:
Proof of ME1, ME2, and ME3 in Token Ring Network:
We can give a formal proof using a proof by contradiction to demonstrate that ME1 (Mutual Exclusion), ME2 (No Deadlock), and ME3 (No Starvation) are satisfied in a token ring network. Because only one node can have the token at a time and so has exclusive access to the shared resource, ME1 is satisfied. ME2 is satisfied since there is no chance of a deadlock because the token is constantly moving throughout the network. Because every node has an equal opportunity to obtain the token, ME3 is satisfied.
Proof of ME1, ME2, and ME3 in Fully Distributed System using Lamport's Algorithm:
Lamport's Algorithm in a fully distributed system satisfies ME1, ME2, and ME3. ME1 is satisfied because processes enter their critical sections in a mutually exclusive manner due to the logical timestamps assigned to each process. Because Lamport's Algorithm ensures that a process in its critical section denotes the conclusion of earlier processes, ME2 is satisfied. Because processes can only access their critical sections after requesting and receiving permission from every other process, ME3 is satisfied.
Proof of ME1, ME2, and ME3 in Fully Distributed System using Ricart and Agrawala's Algorithm:
In a fully distributed system, Ricart and Agrawala's Algorithm also satisfies ME1, ME2, and ME3. ME1 is satisfied because mutual exclusion is ensured by limiting a process's entry into the critical section to those that hold the request priority and have received responses from all other processes. ME2 is satisfied because, in order to avoid deadlock, a process waits for its request to be approved before responding. Because the algorithm guarantees that a process is allowed to enter its critical section fairly and without starvation, ME3 is satisfied.