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Mohamed G. Gouda						CS 356
Summer 2008							Homework 1
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1. 
A protocol involves a process array p[i : 0..n-1] and a process named medium. 
At each instant, any process p[i] can generate a bit(b) message, where b is 
either 0 or 1 and sends it to process medium. When process medium receives a 
bit(b) message from a process p[i], medium sends a copy of the message to each
process in the process array. When a process p[i] receives a bit(b) message 
from process medium, p[i] stores the received b in the next available element 
of its array "rcvd" that is declared as follows:

	var	rcvd : array [integer] of 0..1,
		x    : integer			{index of rcvd; init. 0}

Specify the processes p[i : 0..n-1] and medium using the AP notation. Will
arrays rcvd in all the p[i] processes become identical eventually? Explain
your answer.

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2.
Consider a protocol that consists of three processes p[i : 0..2]. The execution
of this protocol proceeds in an infinite sequence of "rounds". In each round,
each p[i] generates a random value y in the range 0..2 and sends it in a 
data(y) message to each of the other two processes, p[i +3 1] and p[i +3 2], 
in the protocol. After generating one value, in the range 0..2, and receiving
two more values, in the same range, p[i] sums up the three values and takes 
modulo 3 and stores the result in the next available element of its array
"round".

An incomplete specification of process p[i : 0..2] is as follows.

process p[i : 0..2]

inp	J	: set { k | 0<=k<3 ^ k!=i }

var	round	: array [integer] of 0..2,
	x	: integer,			{index of round; init. 0}
	y,z	: 0..2,				{init. 0}
	gen,rcvd: boolean			{init. false}
	j 	: J				{init. j = i +3 1 }

begin
	~gen	         	--> <statement S.0>    
[]	rcv data(y) from p[j] 	--> <statement S.1>
end

Specify statements S.0 and S.1.

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3. 
It is required to generalize the protocol in Problem 2 for the process
array p[i : 0..n-1]. Specify the input and variables in each
p[i] in the generalized protocol.

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