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Byzantine-Tolerant Distributed Grow-Only Sets: Specification and Applications

Authors Vicent Cholvi, Antonio Fernández Anta, Chryssis Georgiou, Nicolas Nicolaou, Michel Raynal, Antonio Russo

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Author Details

Vicent Cholvi
  • Universitat Jaume I, Castelló, Spain
Antonio Fernández Anta
  • IMDEA Networks Institute, Madrid, Spain
Chryssis Georgiou
  • University of Cyprus, Nicosia, Cyprus
Nicolas Nicolaou
  • Algolysis Ltd, Lemesos, Cyprus
Michel Raynal
  • IRISA, Rennes, France
  • Polytechnic University of Hong Kong, Hong Kong
Antonio Russo
  • IMDEA Networks Institute, Madrid, Spain

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Vicent Cholvi, Antonio Fernández Anta, Chryssis Georgiou, Nicolas Nicolaou, Michel Raynal, and Antonio Russo. Byzantine-Tolerant Distributed Grow-Only Sets: Specification and Applications. In 4th International Symposium on Foundations and Applications of Blockchain 2021 (FAB 2021). Open Access Series in Informatics (OASIcs), Volume 92, pp. 2:1-2:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


In order to formalize Distributed Ledger Technologies and their interconnections, a recent line of research work has formulated the notion of Distributed Ledger Object (DLO), which is a concurrent object that maintains a totally ordered sequence of records, abstracting blockchains and distributed ledgers. Through DLO, the Atomic Appends problem, intended as the need of a primitive able to append multiple records to distinct ledgers in an atomic way, is studied as a basic interconnection problem among ledgers. In this work, we propose the Distributed Grow-only Set object (DSO), which instead of maintaining a sequence of records, as in a DLO, maintains a set of records in an immutable way: only Add and Get operations are provided. This object is inspired by the Grow-only Set (G-Set) data type which is part of the Conflict-free Replicated Data Types. We formally specify the object and we provide a consensus-free Byzantine-tolerant implementation that guarantees eventual consistency. We then use our Byzantine-tolerant DSO (BDSO) implementation to provide consensus-free algorithmic solutions to the Atomic Appends and Atomic Adds (the analogous problem of atomic appends applied on G-Sets) problems, as well as to construct consensus-free Single-Writer BDLOs. We believe that the BDSO has applications beyond the above-mentioned problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Grow-only Sets
  • Distributed Ledgers
  • Blockchains
  • Atomic appends


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