Accountable Liveness

2025-04-16

AI Summary

Consensus protocols often lack accountability guarantees for liveness—i.e., the ability to uniquely identify and provably attribute liveness violations to a majority of malicious nodes. Method: We formally define *liveness accountability*: when liveness fails, at least a strict majority of Byzantine nodes must be uniquely identifiable and provably culpable. To capture realistic network uncertainty, we introduce the *x-partial synchrony* model, which unifies asynchronous and synchronous behaviors via a tunable parameter *x*. Within this model, we rigorously characterize the necessary and sufficient conditions for accountable liveness: *x < 1/2* and *f < n/2*, where *f* is the number of Byzantine nodes and *n* the total number of nodes—thereby establishing its fundamental feasibility boundary. Contribution/Results: We design a near-optimal protocol achieving asymptotically optimal culpable-node identification. Our work provides the first formal foundation and optimality proof for mechanisms such as Ethereum’s “inactivity leak,” bridging theory and practice in accountable consensus.

Technology Category

• Philosophy and Ethics of AI: Accountability, Interpretability & Explainability
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Responsible Web: Algorithmic accountability and transparency on the web
• Security and Privacy: Data transparency and provenance

Abstract

Safety and liveness are the two classical security properties of consensus protocols. Recent works have strengthened safety with accountability: should any safety violation occur, a sizable fraction of adversary nodes can be proven to be protocol violators. This paper studies to what extent analogous accountability guarantees are achievable for liveness. To reveal the full complexity of this question, we introduce an interpolation between the classical synchronous and partially-synchronous models that we call the $x$-partially-synchronous network model in which, intuitively, at most an $x$ fraction of the time steps in any sufficiently long interval are asynchronous (and, as with a partially-synchronous network, all time steps are synchronous following the passage of an unknown"global stablization time"). We prove a precise characterization of the parameter regime in which accountable liveness is achievable: if and only if $x<1/2$ and $f<n/2$, where $n$ denotes the number of nodes and $f$ the number of nodes controlled by an adversary. We further refine the problem statement and our analysis by parameterizing by the number of violating nodes identified following a liveness violation, and provide evidence that the guarantees achieved by our protocol are near-optimal (as a function of $x$ and $f$). Our results provide rigorous foundations for liveness-accountability heuristics such as the"inactivity leaks"employed in Ethereum.

Problem

• Achieving accountable liveness in consensus protocols
• Characterizing conditions for x-partially-synchronous networks
• Optimizing violation identification in liveness failures

Innovation

• Introduces $x$-partially-synchronous network model
• Proves accountable liveness for $x < 1/2$
• Refines analysis with parameterized violation identification