Brief announcement: Computing in the presence of weak crash failures

We consider an asynchronous shared memory system of n processes where processes may experience weak crash fail- ures. A crash m-failure is a crash failure of a process that may occurs only while the point contention is at most m. It is known that there is no consensus algorithm for n pro- cesses using registers that can tolerate even a single crash n-failure. Is there a consensus algorithm for n processes us- ing registers that can tolerate a single crash (n..1)-failure? It is known that there is no κ-set consensus algorithm for n > κ processes using registers that can tolerate κ crash n-failures. How may crash (n - l)-failures can a κ-set con- sensus algorithm using registers tolerate, as a function of n, κ and l? Answers to these questions follow from our results regarding the ability to tolerate weak crash failures.