[Paper Review] A Framework for Consistency Models in Distributed Systems

Paulo Sérgio Almeida|arXiv (Cornell University)|Nov 25, 2024

Distributed systems and fault tolerance4 citations

TL;DR

This paper proposes a unified, axiomatic framework for consistency models in distributed systems that generalizes existing models by combining per-process serialization with global visibility, enabling timeless, physically realizable models that support both sequential and concurrent specifications. The key contribution is the CLAM theorem, which establishes a fundamental trilemma (CAL) among Closed past, Arbitration, and Local visibility, revealing inherent tradeoffs in designing wait-free, highly available distributed abstractions.

ABSTRACT

We define am axiomatic timeless framework for asynchronous distributed systems, together with well-formedness and consistency axioms, which unifies and generalizes the expressive power of current approaches. 1) It combines classic serialization per-process with a global visibility. 2) It defines a physical realizability well-formedness axiom to prevent physically impossible causality cycles, while allowing possible and useful visibility cycles, to allow synchronization-oriented abstractions. 3) Allows adding time-based constraints, from a logical or physical clock, either partially or totally ordered, in an optional and orthogonal way, while keeping models themselves timeless. 4) It simultaneously generalizes from memory to general abstractions, from sequential to concurrent specifications, either total or partial, and beyond serial executions. 5) Defines basic consistency axioms: monotonic visibility, local visibility, and closed past. These are satisfied by what we call serial consistency, but can be used as building blocks for novel consistency models with histories not explainable by any serial execution. 6) Revisits classic pipelined and causal consistency, revealing weaknesses in previous axiomatic models for PRAM and causal memory. 7) Introduces convergence and arbitration as safety properties for consistency models, departing from the use of eventual consistency, which conflates safety and liveness. 8) Formulates and proves the CLAM theorem for asynchronous distributed systems: any wait-free implementation of practically all data abstractions cannot simultaneously satisfy Closed past, Local visibility, Arbitration, and Monotonic visibility. While technically incomparable, the CLAM theorem is practically stronger than the CAP theorem, as it allows reasoning about the design space and possible tradeoffs in highly available partition tolerant systems.

Motivation & Objective

• To address the limitations of existing consistency models that either forbid useful visibility cycles or rely on ad hoc axioms, especially for synchronization-oriented abstractions.
• To unify timeless consistency models with time-based constraints (logical or physical clocks) in a modular, orthogonal way.
• To define a general axiomatic framework that supports both sequential and concurrent specifications, including CRDTs and synchronization objects.
• To formalize safety properties like convergence and arbitration independently from liveness, moving beyond eventual consistency.
• To identify and characterize fundamental tradeoffs in designing wait-free, partition-tolerant distributed systems through a new theoretical theorem.

Proposed method

• Introduces a general axiomatic framework based on abstract executions and semantic functions, combining per-process serialization with global visibility.
• Defines three core axioms—monotonic visibility, local visibility, and closed past—as building blocks for consistency models.
• Introduces a physical realizability well-formedness axiom to forbid physically impossible causality cycles while allowing useful visibility cycles.
• Allows optional, orthogonal time constraints (logical or physical clocks) without making models time-dependent.
• Uses the concept of semantic functions to define consistency models that generalize beyond memory to arbitrary data abstractions.
• Proves the CLAM theorem, showing that no wait-free implementation can simultaneously satisfy Closed past, Local visibility, Arbitration, and Monotonic visibility.

Experimental results

Research questions

• RQ1 How can consistency models be unified to support both sequential and concurrent specifications, including synchronization abstractions like barriers?
• RQ2 What axioms are necessary and sufficient to characterize physically realizable consistency models that avoid impossible causality cycles?
• RQ3 How can convergence and arbitration be formalized as safety properties independent of liveness, especially in finite histories?
• RQ4 What are the fundamental tradeoffs in designing wait-free, highly available distributed systems, and how can they be formally characterized?
• RQ5 How does the proposed framework improve upon existing models like PRAM and causal memory by resolving their axiomatic weaknesses?

Key findings

• The framework generalizes classic models by unifying per-process serialization with global visibility, enabling consistent modeling of both memory and general abstractions.
• The physical realizability axiom prevents physically impossible causality cycles while allowing useful visibility cycles, such as those in barrier synchronization.
• The CLAM theorem proves that no wait-free implementation can satisfy Closed past, Local visibility, Arbitration, and Monotonic visibility simultaneously, leading to the CAL trilemma.
• Monotonic visibility is identified as a fundamental and non-negotiable requirement, making the CAL trilemma a practical and stronger constraint than the CAP theorem.
• Convergence is formalized as a universal quantification over executions, distinguishing it from existential eventual consistency and enabling safety reasoning on finite histories.
• The framework enables a new taxonomy of consistency models that clearly illustrates tradeoffs arising from the CAL trilemma, supporting systematic design and comparison of consistency models.