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Algebra of N-event synchronization

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arxiv 2211.00596 v1 pith:GKRPSRQC submitted 2022-11-01 cs.DC cs.DM

Algebra of N-event synchronization

Ernesto Gomez (1) , Keith E. Schubert (2) , Khalil Dajani (1) ((1) California State University San Bernardino , School of Computer Science , Engineering , (2) Baylor University , Department of Electrical , Computer Engineering) This is my paper
classification cs.DC cs.DM
keywords synchronizationalgebraexecutiongomezintroducedmatrixn-eventparallel
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We have previously defined synchronization (Gomez, E. and K. Schubert 2011) as a relation between the times at which a pair of events can happen, and introduced an algebra that covers all possible relations for such pairs. In this work we introduce the synchronization matrix, to make it easier to calculate the properties and results of $N$ event synchronizations, such as are commonly encountered in parallel execution of multiple processes. The synchronization matrix leads to the definition of N-event synchronization algebras as specific extensions to the original algebra. We derive general properties of such synchronization, and we are able to analyze effects of synchronization on the phase space of parallel execution introduced in (Gomez E Kai R, Schubert KE 2017)

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