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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| Vydáno v: | Theoretical computer science Ročník 1024; s. 114914 |
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Elsevier B.V
12.01.2025
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 114914 |
| Author | Gupta, Arya Tanmay Kulkarni, Sandeep S |
| Author_xml | – sequence: 1 givenname: Arya Tanmay orcidid: 0000-0003-2147-8276 surname: Gupta fullname: Gupta, Arya Tanmay email: atgupta@msu.edu – sequence: 2 givenname: Sandeep S surname: Kulkarni fullname: Kulkarni, Sandeep S email: sandeep@msu.edu |
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| Cites_doi | 10.1016/0890-5401(92)90057-M 10.1145/359340.359342 10.1006/jsco.1996.0026 |
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| Keywords | Self-stabilization Multiplication Asynchrony Lattice-linear Modulo |
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| References | Garg (br0060) 2020 Garg (br0070) 2021 Chase, Garg (br0040) 1995 Gupta, Kulkarni (br0080) 2021 Gupta, Kulkarni (br0100) 2023 Zeugmann (br0140) 1992; 96 Bui, Datta, Petit, Villain (br0010) 1999 Gupta, Kulkarni (br0090) 2022 Butler, Sasao (br0020) 2011 Gupta, Kulkarni (br0110) 2023 Garg (br0050) 2022 Cesari, Maeder (br0030) 1996; 21 Rivest, Shamir, Adleman (br0130) Feb 1978; 21 Karatsuba, Ofman (br0120) 1962; 14 Garg (10.1016/j.tcs.2024.114914_br0070) 2021 Garg (10.1016/j.tcs.2024.114914_br0060) 2020 Gupta (10.1016/j.tcs.2024.114914_br0100) 2023 Chase (10.1016/j.tcs.2024.114914_br0040) 1995 Gupta (10.1016/j.tcs.2024.114914_br0110) 2023 Cesari (10.1016/j.tcs.2024.114914_br0030) 1996; 21 Karatsuba (10.1016/j.tcs.2024.114914_br0120) 1962; 14 Rivest (10.1016/j.tcs.2024.114914_br0130) 1978; 21 Bui (10.1016/j.tcs.2024.114914_br0010) 1999 Garg (10.1016/j.tcs.2024.114914_br0050) 2022 Gupta (10.1016/j.tcs.2024.114914_br0080) 2021 Zeugmann (10.1016/j.tcs.2024.114914_br0140) 1992; 96 Butler (10.1016/j.tcs.2024.114914_br0020) 2011 Gupta (10.1016/j.tcs.2024.114914_br0090) 2022 |
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| SubjectTerms | Asynchrony Lattice-linear Modulo Multiplication Self-stabilization |
| Title | Tolerance to asynchrony in algorithms for multiplication and modulo |
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