Tolerance to asynchrony in algorithms for multiplication and modulo

In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms induce a lattice among the global states. Lattice-linearity impli...

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Bibliographic Details
Published inTheoretical computer science Vol. 1024; p. 114914
Main Authors Gupta, Arya Tanmay, Kulkarni, Sandeep S
Format Journal Article
LanguageEnglish
Published Elsevier B.V 12.01.2025
Subjects
Asynchrony
Lattice-linear
Modulo
Multiplication
Self-stabilization
Self-stabilization
Multiplication
Asynchrony
Lattice-linear
Modulo
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Summary:In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms induce a lattice among the global states. Lattice-linearity implies that these algorithms can be implemented in asynchronous environments, where the nodes are allowed to read old information from each other. It means that these algorithms are guaranteed to converge correctly without any synchronization overhead. These algorithms also exhibit snap-stabilizing properties, i.e., starting from an arbitrary state, the sequence of state transitions made by the system strictly follows its specification. •We show that modulo and multiplication are lattice-linear operations.•We study self-stabilizing algorithms for these operations.•Due to lattice-linearity, these algorithms can tolerate asynchrony.•For each problem, the algorithms that we study manifest different lattice structures.•This difference is because they require different numbers of computing nodes.
ISSN:0304-3975
DOI:10.1016/j.tcs.2024.114914