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Mohamed G. Gouda                                        CS 356
Spring      2007                                        Homework 1 Solution
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1. (3 Points):

process c
const n, s

var avail    : array[0..s-1] of 0..3 {initially 3 at each index}
    rqstd    : array[0..n-1, 0..s-1] of boolean
    k        : 0..n-1

par j   : 0..n-1  {corresponding to the clients}
    r   : 0..s-1  {corresponding to the resources}

begin 
    rcv rqst(r) from u[j] -> 
                           if avail[r] > 0 -> avail[r] := avail[r]-1;
                                              send grant(r) to u[j];

                           [] avail[r] = 0 -> rqstd[r,j] := true;
			   fi

[]  rls(r) from u[j] ->
                           k := (j + 1) mod n;
                           do k!=j ^ ~rqstd[r,k] -> k := (k + 1) mod n  od;

                           if rqstd[r,k]  -> rqstd[r,k] := false; send grant(r) to u[k]
                           [] ~rqstd[r,k] -> avail[r] := avail[r] + 1;
                           fi
end


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2. (3 Points):

process p
const 	n
var	ready : boolean,	{initially true}
	i     : 0..n-1
begin
	ready -> i := 0; 
		 do ready -> 
			send rqst to q[i];
			if i<n-1 -> i := i+1
			[] i=n-1 -> ready := false
			fi
		 od;
		 i := 0

[]	rcv rply from q[i] -> if i < n-1 -> i := i+1
			      [] i = n-1 -> ready := true
			      fi

[]      timeout ~ready ^ (#ch.p.q[i] + #ch.q[i].p = 0) -> 
							if i < n-1 -> i := i+1
						        [] i = n-1 -> ready := true
						        fi
end


Specification of process q was not required for the homework but is given below for reference:

process q[i:0..n-1]

begin
	rcv rqst from p -> send rply to p
end

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3. 4 points

process p[i:..m-1]
const   n
var     ready   : boolean {initially true}
        j       : 0..n-1

begin
    ready -> j := any; send rqst(j) to r; ready := false

[]  rcv rply from r -> ready := true 

end

---

process q[j:0..n-1]
const   m
var     i : 0..m-1

begin
     rcv rqst(i) from r -> send rply(i) to r     
end

---

process r
const   m,n
var     x: 0..m-1
        y: 0..n-1

par     i: 0..m-1
        j: 0..n-1
   
begin
       rcv rqst(y) from p[i] -> send rqst(i) to q[y] 

[]     rcv rply(x) from q[j] -> send rply(j) to p[x]

end