Generalized agreement between concurrent fail-stop processes

Abstract

For a system of concurrent processes that can fail by stopping, we study a generalization of the traditional binary agreement problem having more than two possible input values. We provide bounds on the number of possible inputs for which agreement is possible in a system of n concurrent processes that communicate using read-modify-write operations on m shared memory cells of sizes r ₁,...,r _m. Let V be the set of input values. We present an agreement protocol for two processes with ¦V¦≤(Π ^m−1_j=1 r _j)(r _m−1), where r _m=max_j,{r _j}. For m=1 and m=2, we prove that this upper bound on ¦V¦ is the best possible.

A protocol for n processes is fully resilient if it tolerates up to n−1 failures; a fully resilient protocol is wait-free, because no process needs to wait for any other. In a write-once protocol, each memory cell changes value at most once during each execution of the protocol. We present a fully resilient write-once agreement protocol for ¦V¦≤∑ ^m_j=1 (r _j−1). We show that no fully resilient write-once agreement protocol exists when ¦V¦>∑ ^m_j=1 (r _j−1) and n≥m.

Supported by the National Science Foundation under Grant CCR-8922008.