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Mohamed G. Gouda                                        CS 356
Fall 2005                                               Homework 1 Solution
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1. 
Process p can be defined as follows: 

process p
var ready : boolean   {true, initially}

begin
   ready           -> send rqst to q;
                      ready := false

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

[] rcv rqst from q -> if ready  -> send rqst to q;
                                   ready := false
                      [] ~ready -> skip
                      fi; send rply to q;           
end

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2. 
Process c can be defined as follows: 

process c

const n,s

var avail : array [0..s-1] of boolean,        {avail[k]=true where 0<=k<s, initially}
    bff   : array [0..s-1, 0..n-1] of 0..n-1, {circular buffers}
    ns,nr : array [0..s-1] of 0..n-1,         {ns[k]=nr[k] where 0<=k<s, initially}

par j     : 0..n-1,
    r     : 0..s-1

begin
   rcv rqst(r) from u[j] ->
       if avail[r] -> send grant(r) to u[j];
                      avail[r] := false
       []~avail[r] -> bff[r,nr[r]] := j;
                      nr[r] := nr[r] +n 1
       fi

[] rcv rls(r) from u[j] -> 
       if ns[r] = nr[r]  -> avail[r] := true
       [] ns[r] != nr[r] -> send grant(r) to u[bff[r,ns[r]]];
                            ns[r] := ns[r] +n 1
       fi
end

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3. 

process p 

var ready : boolean

begin
    ready ->         {send two new data messages}
	                 ready := false;
 	                 send data(0) to q;
	                 send data(1) to q

[] rcv ack from q -> ready := true

[] timeout (~ready ^ #ch.p.q+#ch.q.p=0) -> {resend data messages}
                                           send data(0) to q;
                                           send data(1) to q

end

process q

var exp : 0 .. 1,  {0, initially}
    i   : 0 .. 1

begin
   rcv data(i) from p -> if exp=i  -> {accept data(i)}
                                      if exp=1  -> send ack to p
                                      [] exp~=1 -> skip
                                      fi; exp := exp +2 1
                         [] exp~=i -> {discard data(i)} 
                                      skip 
                         fi        

[] rcv error          -> skip
end

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4. 
The timeout guard G can be defined as follows:

   wait ^ (#ch.p.q+#ch.q.p=0)