Prasad Jayanti

Fault-tolerant wait-free shared objects

Wait-free implementations of shared objects tolerate the failure of processes, but not the failure of base objects from which they are implemented. We consider the problem of implementing shared objects that tolerate the failure of both processes and base objects. We identify two classes of object failures: <italic>responsive</italic> and <italic>nonresponsive</italic>. With responsive failures, a faulty object responds to every operation, but its responses may be incorrect. With nonresponsive failures, a faulty object may also “hang” without responding. In each class, we define <italic>crash, omission,</italic> and <italic>arbitrary</italic> modes of failure. We show that all responsive failure modes can be tolerated. More precisely, for all responsive failure modes <inline-equation> <f><sc>F</sc></f></inline-equation>, object types <italic>T</italic>, and <italic>t</italic> ω 0, we show how to implement a shared object of type <italic>T</italic> which is <italic>t</italic>-tolerant for <inline-equation> <f><sc>F</sc></f></inline-equation>. Such an object remains correct and wait-free even if up to <italic>t</italic> base objects fail according to <inline-equation> <f><sc>F</sc></f></inline-equation>. In contrast to responsive failures, we show that even the most benign non-responsive failure mode cannot be tolerated. We also show that randomization can be used to circumvent this impossibility result. <italic>Graceful degradation</italic> is a desirable property of fault-tolerant implementations: the implemented object never fails more severely than the base objects it is derived from, even if all the base objects fail. For several failure modes, we show wheter this property can be achieved, and, if so, how.

Time and Space Lower Bounds for Nonblocking Implementations

We show the following time and space complexity lower bounds. Let

f -arrays: implementation and applications

\cal{I}

Robust wait-free hierarchies

be any randomized nonblocking n-process implementation of any object in set A from any combination of objects in set B, where A = {increment, fetch&add, modulo k counter (for any

Efficient and practical constructions of LL/SC variables

k \ge 2n

Every problem has a weakest failure detector

), LL/SC bit, k-valued compare&swap (for any

A time complexity lower bound for randomized implementations of some shared objects

k \ge n

An optimal multi-writer snapshot algorithm

), single-writer snapshot}, and B = {resettable consensus}

Generalized Irreducibility of Consensus and the Equivalence of t -Resilient and Wait-Free Implementations of Consensus

\cup

A Complete and Constant Time Wait-Free Implementation of CAS from LL/SC and Vice Versa

{historyless objects such as registers and swap registers}. The space complexity of