Distributed problem solving in spite of processor failures

Processor failures not leading to a network partition are considered, and the issue of computing associative functions in spite of processor failures is addressed. An intuitive and fundamental result formally proved is that failure detection and computing associative functions are equivalent in faulty networks: one can be performed if and only if the other can be performed. Protocols and impossibility results in various system models are presented in the context of computing associative functions and solving topological problems