Efficient Detection of Global Properties in Distributed Systems using Partial-order Methods

Abstract

A new approach is presented for detecting whether a particular computation of an asynchronous distributed system satisfies $\Poss\Phi$ (read ``possibly $\Phi$''), meaning the system could have passed through a global state satisfying predicate $\Phi$, or $\Def\Phi$ (read ``definitely $\Phi$''), meaning the system definitely passed through a global state satisfying $\Phi$. Detection can be done easily by straightforward state-space search; this is essentially what Cooper and Marzullo proposed. We show that the persistent-set technique, a well-known partial-order method for optimizing state-space search, provides efficient detection. The resulting detection algorithms handle larger classes of predicates and thus are more general than two special-purpose detection algorithms by Garg and Waldecker, which detect $\Poss\Phi$ and $\Def\Phi$ efficiently for a restricted but important class of predicates. Furthermore, our algorithm for $\Poss\Phi$ achieves the same worst-case asymptotic time complexity as Garg and Waldecker's special-purpose algorithm for $\Poss\Phi$. We apply our algorithm for $\Poss\Phi$ to two examples, achieving a speedup of over 700 in one example and over 70 in the other, compared to unoptimized state-space search.