arXiv subjects

David Lehnherr

Publications and source records attributed to David Lehnherr.

6 recordsLinked to original sources

arXiv2026

The Consensus Number of Untraceable Cryptocurrencies

Sender untraceability hides the account spent by a cryptocurrency transfer among a set of candidates, its masking set. What a transfer does to that set separates two designs: classical schemes retain the whole set and append a nullifier marking the spent account, so the ledger grows with every transfer; constant-state schemes instead consume and replace the entire set. We ask how this choice affects synchronization. We formalize the two designs as the linear and constant untraceable asset transfer objects (LUAT and CUAT) and locate them in the consensus hierarchy. In LUAT, transfers from distinct accounts commute. Its consensus number is 2, compared with 1 for standard asset transfer, independently of the masking-set size and of the untraceability notion, and LUAT is starvation-free. Partitioning the accounts into fixed masking sets lets exhausted sets be garbage-collected without increasing that number. In CUAT, a transfer consumes and replaces every account of its masking set, so two transfers whose sets intersect cannot both take effect. We formalize this with the conflict graph on masking sets, whose edges join sets sharing an account. Under weak untraceability, which protects a transaction in isolation, the consensus number is unbounded already for one-round protocols. Under strong untraceability, which protects against an observer of the complete history, untraceability holds on a history exactly when any two accounts sharing a masking set occur in the same number of the masking sets in it. This uniform incidence bounds the conflict graph, and matching constructions attain it, so the consensus number is determined exactly and grows quadratically in the masking-set size. Finally, CUAT is not starvation-free. The two objects therefore pay for the same privacy differently: LUAT in storage, CUAT in synchronization and fairness.

cs.DC↗

arXiv2026

An Epistemic Analysis of Random Coordinated Attack

The coordinated attack problem models the challenge of coordinating a joint action within a bounded time by communicating over unreliable links. It was the first distributed computing problem proven unsolvable. Its analysis also revealed the importance of common knowledge, a central concept in epistemic logic. However, the randomized version of coordinated attack, which is solvable, has not, to the best of our knowledge, been studied through the lens of probabilistic epistemic logic, where processes generate randomness by flipping coins. We present an epistemic logic framework for studying randomized algorithms that execute for a bounded number of rounds. The framework applies to coordinated attack, approximate agreement, and consensus, and supports dynamic graph models: synchronous systems in which reliable processes execute a bounded number of rounds while an adversary determines which messages are lost. Our approach combines techniques from the logical characterization of dynamic networks and task solvability with ideas from probabilistic dynamic epistemic logic. It is inspired by the operational model of Varghese and Lynch for randomized coordinated attack. More broadly, the resulting notion of probabilistic epistemic task solvability provides a foundation for the epistemic study of randomized distributed computation. Using this framework, we analyze the Varghese-Lynch algorithm from a knowledge-theoretic perspective, providing a formal treatment of the algorithm and its lower bound. As a byproduct, we strengthen the lower bound and show it is tight. The proof relies on indistinguishability arguments, demonstrating that reasoning about knowledge remains essential in the probabilistic setting. We also formalize the notion of information level introduced by Varghese and Lynch, showing that it corresponds to a specific epistemic formula.

cs.DC↗

arXiv2026

Simplicial Belief

Recently, much work has been carried out to study simplicial interpretations of modal logic. While notions of (distributed) knowledge have been well investigated in this context, it has been open how to model belief in simplicial models. We introduce polychromatic simplicial complexes, which naturally impose a plausibility relation on states. From this, we can define various notions of belief.

cs.LO↗

arXiv2025

Hypergraph Semantics for Doxastic Logics

Simplicial models have become a crucial tool for studying distributed computing. These models, however, are only able to account for the knowledge, but not for the beliefs of agents. We present a new semantics for logics of belief. Our semantics is based on directed hypergraphs, a generalization of ordinary directed graphs in which edges are able to connect more than two vertices. Directed hypergraph models preserve the characteristic features of simplicial models for epistemic logic, while also being able to account for the beliefs of agents. We provide systems of both consistent belief and merely introspective belief. The completeness of our axiomatizations is established by the construction of canonical hypergraph models. We also present direct conversions between doxastic Kripke models and directed hypergraph models.

cs.LO↗

arXiv2024

Synergistic Knowledge

In formal epistemology, group knowledge is often modelled as the knowledge that the group would have, if the agents shared all their individual knowledge. However, this interpretation does not account for relations between agents. In this work, we propose the notion of synergistic knowledge which makes it possible to model those relationships.

cs.LO↗

arXiv2023

A logic of interactive proofs

We introduce the probabilistic two-agent justification logic IPJ, a logic in which we can reason about agents that perform interactive proofs. In order to study the growth rate of the probabilities in IPJ, we present a new method of parametrising IPJ over certain negligible functions. Further, our approach leads to a new notion of zero-knowledge proofs.

cs.LO↗