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<p><b>Abstract</b>—Specifying and detecting predicates in a distributed execution is an important problem. Distributed execution observation has classically used two modalities—<tmath>\big. Possibly(\phi)\bigr.</tmath> and <tmath>\big. Definitely(\phi)\bigr.</tmath>—for predicate <tmath>\big. \phi\bigr.</tmath>. Based on the temporal interactions of intervals, the author identified a complete, <it>orthogonal</it> set of relationships <tmath>\big. \Re\bigr.</tmath> between pairs of intervals in a distributed execution. This paper shows how to map the rich, orthogonal classification of modalities of pairwise interval interactions, to the classical coarse-grained classification, <tmath>\big. Possibly(\phi)\bigr.</tmath> and <tmath>\big. Definitely(\phi)\bigr.</tmath>, for specifying predicates defined on any number of processes. This increases the power of expressing the temporal modalities under which predicates can be specified, beyond the current <tmath>\big. Possibly\bigr.</tmath>/<tmath>\big. Definitely\bigr.</tmath> classification. This paper also gives timestamp-based tests for the orthogonal modalities in the refined classification.</p>
Predicates, causality, synchronization, distributed execution, distributed system, global state.

A. D. Kshemkalyani, "A Fine-Grained Modality Classification for Global Predicates," in IEEE Transactions on Parallel & Distributed Systems, vol. 14, no. , pp. 807-816, 2003.
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