From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Sun, 12 Jun 2011 17:06:48 +0000 (+0530)
Subject: solution to 3.43
X-Git-Url: https://git.rkrishnan.org/pf/content/en/seg/about//%22%22?a=commitdiff_plain;h=18a68c77ee356f3dcfa1f9711f892571d1580b83;p=sicp.git

solution to 3.43
---

diff --git a/src/sicp/ex3_43.rkt b/src/sicp/ex3_43.rkt
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+#lang racket
+
+#|
+
+;; Argue that if the processes are run sequentially, after any number of 
+;; concurrent exchanges, the account balances should be $10, $20, and $30 
+;; in some order. 
+
+Support a1, a2 and a3 are the 3 accounts with the balances $10, $20 and $30
+respectively. Now the operations involved in the serialized exchange are:
+(in order)
+
+(serialized-exchange a1 a2)
+
+1. acquire serializer s1 for a1
+2. acquire serializer s2 for a2
+3. create serialized exchange procedure using s2
+4. create serialized exchange procedure using s1
+5. apply the resulting procedure of step 4 to a1 and a2.
+
+Now, if we have two concurrent serialized exchange procedure running, one
+of them is (serialized-exchange a1 a2) and the other is 
+(serialized-exchange a1 a3), then the following is one possibility.
+
+1. procedure 1 (called p1 from here after) acquires s1. 
+2. p2 also tries to acquire s1 but since p1 has already acquired it, it waits.
+3. p1 proceeds with the exchange. resulting in a swapped exchange of balance
+   with a1 having 20 and a2 having 10.
+4. At this point, s1 is released and p2 acquires s1. It proceeds to do the
+   exchange, resulting in exchange of 20 and 30.
+5. End result is: a1 = 30, a2 = 10, a3 = 20.
+
+;; Draw a timing diagram like the one in figure 3.29 to show how this 
+;; condition can be violated if the exchanges are implemented using the 
+;; first version of the account-exchange program in this section.
+
+Without serializer, the exchange procedure involves the following steps.
+
+1. get balance of account1
+2. get balance of account2
+3. find difference between 1 and 2.
+4. withdraw the difference from account1
+5. deposit the difference to account2
+
+When two concurrent exchange procedures (exchange a1 a2) and (exchange a1 a3)
+are running, the following can happen.
+
+1. p1 gets balance of a1 (10).
+2. p2 gets balance of a1 (10).
+3. p1 gets balance of a2 (20).
+4. p2 gets balance of a3 (30).
+5. p1 calculates difference (-10).
+6. p2 calculates difference (-20).
+7. p1 withdraws -10 from a1 (20).
+8. p2 withdraws -20 from a1 (40).
+9. p1 deposits -10 to a2 (10)
+10. p2 deposits -20 to a3 (10)
+
+At the end, a1 = 40, a2 = 10, a3 = 10
+
+;; On the other hand, argue that even with this exchange program, the sum of 
+;; the balances in the accounts will be preserved. 
+
+(see above. We can try with different interspersing of operations. Note that
+the above steps assume that withdrawals and deposits and balance operations
+are 'atomic')
+
+;; Draw a timing diagram to show how even this condition would be violated 
+;; if we did not serialize the transactions on individual accounts. 
+
+It is obvious that this will be violated. For example, withdraw operation
+involves (set! balance (- balance amount)) and deposit operation involves
+(set! balance (+ balance amount)). It could be that, after the target
+balance is calculated for an account, a new balance amount is set which
+is reset by the previously calculated value of balance. This is a non-linear
+operation and not a composition. 
+
+|#
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