CEG 730 Distributed Computing Principles Fall 2009// Final Exam // 120 minutes // 100 points Prabhaker Mateti

This is a closed book, closed notes exam. Do not give or take help during the exam. Turn in your answers using the command: ~ceg73000/bin/turnin FI answers.txt

1. (12*5 points) In the following, it is possible to write between 5 to 10 sentences each, and yet receive full score.
   1. In the context of token-passing algorithms, what is a "token"?
   2. Token-passing algorithms were discussed under the heading of asynchronous message passing. Is it because token-passing does not make sense under synchronous message passing? Discuss.
   3. Construct the ssend(pid, msg) and srecv(pid, msg) primitives of synchronous message passing from asend(pid, msg) and arecv(pid, msg) primitives of asynchronous message passing.
   4. Explain the Satisfaction Rule for Synchronous Communication.
   5. The happened before relation, as discussed, requires a logical clock for every process. But a typical machine (node) in a distributed system runs several processes. Is it sufficient to maintain a logical clock per node that is shared by all processes running on that node? Show by construction or discuss why this does not work.
   6. In the context of distributed semaphore implementation, discuss "fully acknowledged" messages.
   7. Can any solution to the distributed mutual exclusion problem be thought of as a solution to the problem of implementing semaphores in a distributed system, and vice versa? True/False? Discuss.
   8. A binary "tree" is here given as a collection of its node contents: (1, 2, 3), (2, 0, 3), (3, 2, 4), (4, 2, 1). Each node contents is a triplet of (info-integer, left-link, right-link). The node with info integer 1 is the root. Null links are 0. Marshal/serialize the given binary tree.
   9. Reconstruct the binary "tree" serialized below. List each node as a triplet of (info-integer, left-link, right-link), as usual. The first digit in the sequence is the offset of the root node.

      	  marshaled sequence: 2 1 0 5 2 7 3 0 A 4 2 5 0
      	  offsets in hex:     1 2 3 4 5 6 7 8 9 A B C D

   10. Does the precondition and statement {x ≥ 4 } < x := x - 4 > interfere with the triple
       {x ≥ 10} < x := x + 5 > {x ≥ 12}.
   11. Using the technique of weakened assertions, prove that {x = 0} S {x = 0} is a theorem, where S is var x := 0; co <x := x+2> || <x := x+3> || <x := x - 5> oc
   12. Explain, with an example, the map/reduce idea behind Hadoop.
2. (10+20+10 points) Given a large (in the zillions) bag B of integers, and a specific integer x, compute how many of B's integers are (i) greater than x, (ii) equal to x, and (iii) less than x. Two solutions, one in CSP and another in C-Linda are to be developed. It is not required that both use the same "idea." Present your solutions with full explanations.
   1. As usual, (i) we wish to maximize concurrency, (ii) we prefer a symmetric solution, (iii) we rate correctness much higher than efficiency, and cannot tolerate (iv) deadlocks or (v) livelocks. Defend why for each of these five.
   2. For C-Linda, assume that the tuple space already contains the bag of integers < "B", n>, the size of this bag < "BSZ", bsz>, and < "x", x>. You lose 5 points for each use of inp or rdp. Choose a number of processes that maximizes concurrency. At the end, we expect to see three tuples: < "greater", g >, < "equal", e >, and < "lesser", l >.
   3. For CSP, the bag is generated by process B whose structure is B :: *[ ... --> P!m ]. Assume that the first two numbers output are bsz and x; the rest are integers of B. Develop the process P and appropriately chosen other processes, if any.