
Briefing
Traditional distributed consensus models fail to capture the unique challenges of permissionless blockchains, where participants are unknown, can join or leave at will, and can operate multiple identities. This lack of formal understanding hinders robust protocol design. This paper introduces a novel hierarchy of “degrees of permissionlessness,” formally defining distinct settings (fully permissionless, dynamically available, quasi-permissionless) based on a protocol’s knowledge of participants.
Within this framework, it rigorously proves possibility and impossibility results for achieving consensus properties like safety and liveness. This new theoretical lens provides a critical tool for designing and evaluating blockchain protocols, enabling a precise understanding of the fundamental assumptions required for secure and resilient decentralized systems.

Context
Before this research, the study of distributed consensus largely focused on “permissioned” settings, where the set of participants is known and relatively stable. Blockchain protocols, however, operate in a “permissionless” environment, introducing challenges like unknown participants, dynamic activity, and Sybil attacks. This fundamental shift from permissioned to permissionless operation meant that existing theoretical models were insufficient to rigorously analyze the security and liveness properties of systems like Bitcoin and Ethereum, leading to a gap in formal understanding of their true capabilities and limitations.

Analysis
The paper’s core mechanism is a conceptual framework that systematically models the “permissionless setting” by introducing a hierarchy of three distinct environments. The fully permissionless setting assumes no knowledge about current participants, characteristic of Proof-of-Work. The dynamically available setting assumes knowledge of a dynamically evolving list of potential participants, typical of Proof-of-Stake longest-chain protocols. The quasi-permissionless setting assumes all potential participants are active, akin to Proof-of-Stake PBFT-style protocols.
This framework fundamentally differs from previous approaches by precisely parameterizing the “degree of permissionlessness” and then deriving specific possibility and impossibility results for Byzantine agreement and state machine replication within each defined setting. This allows for a rigorous, comparative analysis of different blockchain consensus paradigms based on their underlying assumptions.

Parameters
- Core Concept ∞ Degrees of Permissionlessness Hierarchy
- Key Authors ∞ Andrew Lewis-Pye, Tim Roughgarden
- Publication Date ∞ April 28, 2023
- Canonical Identifier ∞ arXiv:2304.14701
- Settings Defined ∞ Fully Permissionless, Dynamically Available, Quasi-Permissionless
- Challenges Addressed ∞ Unknown Players, Player Inactivity, Sybil Attacks
- Fundamental Problems ∞ Byzantine Agreement, State Machine Replication

Outlook
This foundational framework opens new avenues for rigorous research into the design space of blockchain protocols. Future work will likely involve applying this hierarchy to analyze emerging consensus mechanisms, exploring the precise trade-offs between different degrees of permissionlessness, and developing new protocols that optimally leverage specific assumptions about participant knowledge and activity. In the next 3-5 years, this theoretical understanding could lead to the development of more robust, provably secure, and economically sustainable blockchain architectures, enabling the creation of decentralized applications with clearer guarantees regarding their liveness and safety in increasingly complex and adversarial environments.

Verdict
This research provides an indispensable theoretical framework, fundamentally redefining the understanding of permissionless consensus and establishing critical boundaries for blockchain security and liveness.