Tree Locking On Changing Trees

Cover Tree Locking On Changing Trees
Tree Locking On Changing Trees
Vladimir Lanin
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By definition of deadlock-prone state, a, ->-> a(, +i)mod n by the path from p, to c, . Thus, flo => flo. Which contradicts lemma 7. D As with serializability, problems arise when we try to extend this result to compulations containing readers. In fact, as illustrated by Fig. 8, even a segregated computation satisfying the original (non- dynamic) tree protocol and the transitive conflict rule may reach a deadlock-prone stale. Thus, to guaran- tee deadlock freedom, we need to enforce some variat...ion of the transitive conflict rule, such as: For any state s, if w — >-> r — >-^ w' where r is a reader and w ^ w', then w — »-> w' must also hold.
s s s + It is easily shown by an argument similar to the proof of lemma 8 that this guarantees that — >-» stays irreflexive in all states, thus making a deadlock-prone state impossible. We should also note that the methods mentioned above for enforcing the transitive conflict rule also work to enforce this variation.
8. Order Preservation We say that action a completely precedes action b ii a releases all its locks before b places its first lock.


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