$1.$ Consider below Figure that shows three processes $($P$1,$ P$2,$ P$3)$ with events

$($e$1,$e$2,...$e$12)$ and messages communicating between them. Assume that

initial logical clock values are all initialized to $0.$

a$.$ List the Lamport Logical timestamps for each event shown in Figure.

Assume that each process maintains a logical clock as a single integer

value as a Lamport clock. Provide timestamps for each labeled event.

b$.$ determine all the events that happen before event e$8($as

per Lamport$$s Happened$-$Before relation$).$ Also determine the events

that are concurrent with event e$8$

$2.$ Three computers, A$,$ B$,$ and C communicate using a protocol that

implements Lamport Vector clocks $,$at the beginning all vector clocks are

set to $[0,0,0,]$ the following sequence of events occurs:

$$ A sends message M$1$ to B

$$ C sends message M$2$ to B

$$ B receives M$2$ before M$1$

$$ B replies message M$3$ to C first, and then message M$4$ to A

$$ After receiving message M$3,$ C sends message M$5$ to A

$$ After receiving message M$5,$ A sends message M$6$ to B

$$ After receiving message M$6,$ B sends message M$7$ to A

$$ The last message A receive is M$4$

Provide the Lamport vector clock timestamps for each of these events.