Algebra of data reconciliation

0569846 - ÚTIA 2023 RIV HU eng J - Journal Article
Csirmaz, E. P. - Csirmaz, Laszlo
Algebra of data reconciliation.
Studia Scientiarum Mathematicarum Hungarica. Roč. 59, 3-4 (2022), s. 209-231. ISSN 0081-6906. E-ISSN 1588-2896
R&D Projects: GA ČR(CZ) GA19-04579S
Institutional support: RVO:67985556
Keywords : file synchronization * algebraic model * confluence * rewriting system
OECD category: Pure mathematics
Impact factor: 0.7, year: 2022
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2023/SI/csirmaz-0569846-preprint.pdf https://akjournals.com/view/journals/012/59/3-4/article-p209.xml

With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation – bringing two replicas of the same data structure as close as possible without overriding local changes – is investigated in an algebraic model. Our approach is to consider two sequences of simple commands that describe the changes in the replicas compared to the original structure, and then determine the maximal subsequences of each that can be propagated to the other. The proposed command set is shown to be functionally complete, and an update detection algorithm is presented which produces a command sequence transforming the original data structure into the replica while traversing both simultaneously. Syntactical characterization is provided in terms of a rewriting system for semantically equivalent command sequences. Algebraic properties of sequence pairs that are applicable to the same data structure are investigated. Based on these results the reconciliation problem is shown to have a unique maximal solution. In addition, syntactical properties of the maximal solution allow
for an efficient algorithm that produces it.
Permanent Link: https://hdl.handle.net/11104/0341180