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Mohamed G. Gouda						CS 356
Summer 2008							Midterm 3
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60 minutes 							Open Book
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1. (10 points) 
A protocol involves the processes: p, q, and r[i : 0..n-1]. In this protocol,
process q is the only neighbor of process p, and the only neighbor of each 
process r[i]. The function of this protocol is to allow process p to maintain 
a boolean array net[i : 0..n-1] such that the value of each element net[i] in
the array is true iff all the channels between process p and process r[i] are 
up. An incomplete specification of processes p and q follows:

	process p
	const	n
	inp	up	: boolean 	{two channels between} 
					{p and q are both up?}
	var	net	: array [0..n-1] of boolean,
		v	: array [0..n-1] of boolean,
		ts, t	: integer,	{init. 0}
		m	: 0..n
	begin
		...
	end

	process q
	const	n
	inp	up	: boolean,	{two channels between}
					{p and q are both up?}
		upr	: array [0..n-1] of boolean
					{two channels between}
					{q and each r[i] are up?}
	var	ts	: integer	{init. 0}
	begin
		up	--> ...
	end
	
Complete the specifications of p and q.

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2. (10 points)
A routing protocol involves the processes p[i : 0..m-1, j : 0..n-1] where
each process p[i,j] is said to "belong to group i". The processes generate
data messages and route them. Each generated data message has one field x in 
the range 0..m-1. The ultimate destination of a generated data(x) message is
any process p[x,j] that belongs to group x. Each process p[i,j] has three 
input arrays 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
		grp	: array [0..m-1] of N

The value of grp[x] is the indices of the best neighbor of p[i, j] for 
reaching a process that belongs to group x. Specify process p[i,j].
 
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