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A significant portion of research on distributed ledgers has focused on circumventing the limitations of leader-based blockchains mainly in terms of scalability, decentralization and power consumption. Leaderless architectures based on directed acyclic graphs (DAGs) avoid many of these limitations altogether, but their increased flexibility and performance comes at the cost of increased design complexity, so their potential has remained largely unexplored. Management of write access to these ledgers presents a major challenge because ledger updates may be made in parallel, hence transactions cannot simply be serialised and prioritised according to token fees paid to validators. In this work, we propose an access control scheme for leaderless DAG-based ledgers which is based on consuming credits rather than paying fees in the base token. We outline a general model for this new approach and provide some simulation results showing promising performance boosts., Comment: Short version awarded with the Best Paper Award at BLOCKCHAIN Congress 2023

The robust construction of the ledger data structure is an essential ingredient for the safe operation of a distributed ledger. While in traditional linear blockchain systems, permission to append to the structure is leader-based, in Directed Acyclic Graph-based ledgers, the writing access can be organised leaderless. However, this leaderless approach relies on fair treatment of non-referenced blocks, i.e. tips, by honest block issuers. We study the impact of a deviation from the standard tip selection by a subset of block issuers with the aim of halting the confirmation of honest blocks entirely. We provide models on this so-called orphanage of blocks and validate these through open-sourced simulation studies. A critical threshold for the adversary issuance rate is shown to exist, above which the tip pool becomes unstable, while for values below the orphanage decrease exponentially. We study the robustness of the protocol with an expiration time on tips, also called garbage collection, and modification of the parent references per block., Comment: IEEE ICBC 2023

Voting algorithms have been widely used as consensus protocols in the realization of fault-tolerant systems. These algorithms are best suited for distributed systems of nodes with low computational power or heterogeneous networks, where different nodes may have different levels of reputation or weight. Our main contribution is the construction of a fair voting protocol in the sense that the influence of the eventual outcome of a given participant is linear in its weight. Specifically, the fairness property guarantees that any node can actively participate in the consensus finding even with low resources or weight. We investigate effects that may arise from weighted voting, such as loss of anonymity, centralization, scalability, and discuss their relevance to protocol design and implementation., Comment: conference paper, SAI Computing21. arXiv admin note: text overlap with arXiv:2006.00928

The fast probabilistic consensus (FPC) is a voting consensus protocol that is robust and efficient in Byzantine infrastructure. We propose an adaption of the FPC to a setting where the voting power is proportional to the nodes reputations. We model the reputation using a Zipf law and show using simulations that the performance of the protocol in Byzantine infrastructure increases with the Zipf exponent. Moreover, we propose several improvements of the FPC that decrease the failure rates significantly and allow the protocol to withstand adversaries with higher weight. We distinguish between cautious and berserk strategies of the adversaries and propose an efficient method to detect the more harmful berserk strategies. Our study refers at several points to a specific implementation of the IOTA protocol, but the principal results hold for general implementations of reputation models.

We consider a one dimensional ballistic nearest-neighbor random walk in a random environment. We prove an Erd\H{o}s-R\'enyi strong law for the increments., Comment: 43 pages

We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin, which makes them transient. We also compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements' local time for sites far from the origin and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements' local times., Comment: 32 pages

We study a model of rumor propagation in discrete time where each site in the graph has initially a distinct information; we are interested in the number of "conversations" before the entire graph knows all informations. This problem can be described as a flooding time problem with multiple liquids. For the complete graph we compare the ratio between the expected propagation time for all informations and the corresponding time for a single information, obtaining the asymptotic ratio $3/2$ between them., Comment: 13 pages, 1 figure