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Mohamed G. Gouda						Midterm 3
CS 356: Computer Networks					Summer 2007
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Open Book							60 Minutes
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1. (10 points)

The processes in a network p[i:0..n-1] are arranged in a unidirectional ring,
where there is one channel from each process p[i] to process p[i +n 1]. Thus,
each p[i] can receive messages only from p[i -n 1] and can send messages only
to p[i +n 1]. The processes circulate only one chk message around the ring, and
when this message is lost, process p[0] generates a new chk message that 
circulates around the ring. Each process p[i] has a boolean variable "up" whose
value is assigned true, when and only when all the channels in the network are 
up. The processes in this network are specified as follows:

process p[i : 1..n-1]
var   up : boolean,
      b  : 0..1
begin
   rcv chk(b) from p[i -n 1]  -> S.0
[] rcv error  from p[i -n 1]  -> skip
[] timeout (Forall i, 0 <= i < n, #ch.p[i].p[i +n 1] = 0)   -> S.1
end

process p[0]
const n
var   up : boolean,
      b  : 0..1
begin
   rcv chk(b) from p[n-1]  -> S.2
[] rcv error  from p[n-1]  -> skip
[] timeout (Forall i, 0 <= i < n, #ch.p[i].p[i +n 1] = 0) ^ 
           (Forall i, 1 <= i < n, up.p[i] = false)           -> S.3
end

Specify statements S.0, S.1, S.2, S.3.
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2. (10 points)

A network p[i : 0..m-1, j : 0..n-1] consists of m regions of n processes each.
The processes in this network generate data(x,y) messages and route them to 
their ultimate destinations, using hierarchical routing. The ultimate 
destination of each data(x,y) message is process p[x,y]. In each region i, 
process p[i,0] is "the gateway". This means that data messages that enter or
leave region i do so by going through process p[i,0]. The gateways for each
pair of regions are neighbors. Thus a data(x,y) that is generated in region i
first travels in region i until it reaches p[i,0], then goes to p[x,0], then
travels in region x until it reaches p[x,y]. A process in this network is 
specified as follows.

process p[i : 0..m-1, j : 0..n-1]
inp N   : set{(i',j') | p[i',j'] is a neighbor of p[i,j]}
    up  : array [N] of boolean
    prs : array [0..n-1] of N
var x   : 0..m-1, y : 0..n-1
par g   : N
begin
   true -> x, y := any, any; RTMSG
[] rcv data(x,y) from p[g] -> RTMSG
end

Specify statement RTMSG.
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