Efficient Detection of Global Properties in Distributed Systems Using Partial-Order Methods

A new approach is presented for detecting whether a particular computation of an asynchronous distributed system satisfies \(\mathop{{\bf Poss}}\Phi\) (read “possibly Φ”), meaning the system could have passed through a global state satisfying predicate Φ, or \(\mathop{{\bf Def}}\Phi\) (read “definitely Φ”), meaning the system definitely passed through a global state satisfying Φ. 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. This approach achieves the same worst-case asymptotic time complexity as two special-purpose detection algorithms of Garg and Waldecker that detect \(\mathop{{\bf Poss}}\Phi\) and \(\mathop{{\bf Def}}\Phi\) for a restricted but important class of predicates. For \(\mathop{{\bf Poss}}\Phi\), our approach applies to arbitrary predicates and thus is more general than Garg and Waldecker’s algorithm. We apply our algorithm for \(\mathop{{\bf Poss}}\Phi\) to two examples, achieving a speedup of over 700 in one example and over 70 in the other, compared to unoptimized state-space search.