# Combining tentative and definite executions for very fast i)ependable parallel computing

## Abstract

We present a general and efficient strategy for computing mtustly on unreliable parallel machines. The model of a parallel machine that we use is a CRCW PRAM with dynamic resource fluctuations: processors can fail during the computation, and may possibly bc restored later. We first introduce the notions of dejinite and tentatitie algorithms for executing a single parallel step of an ideal parallel machine on the unreliable machine. A definite algorithm is one that guarantees a correct execution of a step, while a tentative algorithm is one that is "highly likely" to produce a correct execution of a step on the unreliable machine. We show that any definite execution of one step requires Cl(log n) time on an∗processor unreliable machine, even if all the processors functioned perfectly, This implies an l(log n) slowdown for executing any non-Trivial program on the unreliable machine, provided only definite executions are used. We get around this overhead by combining tentative and definite execution schemes appropriately, to derive correct and efllcient robust executions for arbitrary PRAM programs, with expected amortized slowdown of only 0(1) for a variety of reasonable failure models. We adeve this by using a tentative algorithm to execute each of the program's steps, while using a definite algorithm to audit the execution at selected points. If the audit does not certify the execution as correct, then the execution is rolled back to a previous audit point and restarted from there. In contrast to this work, all previous results required a slowdown of Cl(log n), since they used definite algorithms only.