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Unformatted text preview: FIFO Queues Corollary 5.4.1 : It is impossible to construct a watfree implementation of a queue, stack priority queue, set or list from a set of atomic registers. Theorem 5.4.1 : FIFO queues have consensus number 2. FIFO Queues Proof: By contradiction. Assumptions: ● We have a consensus protocol for threads A, B and C; ● The protocol has a critical state s; ● A's next move leads to a 0valent state; ● B's next move leads to a 1valent state. FIFO Queues s'' s A deq 1 B deq A deq B deq s' C runs solo C runs solo FIFO Queues ● Suppose: A enq(a) and B deq() ● If the queue is nonempty, the methods commute and C cannot observe the order in which they occurred; ● If the queue is empty, the 1valent state (B deq() and A enq(a) ) is indistinguishable from the 0valent state (A enq(a) ). s'' s A enq(a) B enq(b) A enq(a) B enq(b) s' C runs solo 1 C runs solo run A until deq a run A until deq b run B until deq b run B until deq a...
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 Spring '10
 KLAZAR

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