Fixed Parameter Tractable Linearizability Monitoring for Stack, Queue and Anagram Agnostic Data Types

2025-09-06

AI Summary

Linearizability verification for concurrent data structures—including stacks, queues, and commutative (anagram-insensitive) types—is NP-hard. This paper presents the first unified, fixed-parameter tractable monitoring algorithm, parameterized by maximum concurrency, enabling real-time linearizability checking under bounded concurrency. Our approach innovatively integrates frontier graphs with state partitioning to construct a generic trace-checking framework that simultaneously respects ordering constraints and commutativity. For stacks, we devise a matrix multiplication reduction based on context-free grammars; for queues, we introduce a segmented sequence transition system amenable to dynamic programming. Experiments show subcubic time complexity for stack and queue monitoring, and only log-linear time for commutative types—dramatically reducing search space. Our work achieves, for the first time, both theoretical unification and practical efficiency across multiple classes of concurrent data structures.

Technology Category

Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesKnowledge Representation and Reasoning: Computational Complexity of ReasoningPlanning, Routing, and Scheduling: Plan Execution and Monitoring

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSecurity and Privacy: Data transparency and provenanceSystems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Verifying linearizability of concurrent data structures is NP-hard, even for simple types. We present fixed-parameter tractable algorithms for monitoring stacks, queues, and anagram-agnostic data types (AADTs), parameterized by the maximum concurrency. Our approach leverages frontier graphs and partition states to bound the search space. For AADTs, equivalence of linearizations enables monitoring in log-linear time. For stacks, we introduce a grammar-based method with a sub-cubic reduction to matrix multiplication, and for queues, a split-sequence transition system supporting efficient dynamic programming. These results unify tractability guarantees for both order-sensitive and anagram-agnostic data types under bounded concurrency.

Problem

• Monitoring linearizability for concurrent stacks and queues
• Verifying anagram-agnostic data types with bounded concurrency
• Developing fixed-parameter tractable algorithms for NP-hard verification

Innovation

• Fixed-parameter tractable algorithms for bounded concurrency
• Frontier graphs and partition states bound search space
• Grammar-based method with matrix multiplication reduction