Prefix Trees Improve Memory Consumption in Large-Scale Continuous-Time Stochastic Models

2025-12-19

AI Summary

To address the memory bottleneck arising from state-space explosion in continuous-time Markov chains (CTMCs)—particularly in large-scale chemical reaction networks (CRNs)—this paper introduces, for the first time, prefix trees (Tries) to replace conventional hash tables in CTMC transient probability analysis. The approach integrates bounded model checking (BMC) to optimize variable ordering, thereby enhancing structural sharing efficiency. It supports general symbolic CTMC modeling and analysis, achieving up to 73% memory reduction over hash-table-based methods on models with over 100 million states, significantly surpassing the scalability limits of existing tools. The core contributions are: (i) a Trie-based compact state encoding scheme for CTMCs, and (ii) a BMC-driven framework for optimizing variable ordering to maximize sharing. Together, these innovations establish a novel, efficient, and highly scalable paradigm for formal verification of ultra-large stochastic systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Highly-concurrent system models with vast state spaces like Chemical Reaction Networks (CRNs) that model biological and chemical systems pose a formidable challenge to cutting-edge formal analysis tools. Although many symbolic approaches have been presented, transient probability analysis of CRNs, modeled as Continuous-Time Markov Chains (CTMCs), requires explicit state representation. For that purpose, current cutting-edge methods use hash maps, which boast constant average time complexity and linear memory complexity. However, hash maps often suffer from severe memory limitations on models with immense state spaces. To address this, we propose using prefix trees to store states for large, highly concurrent models (particularly CRNs) for memory savings. We present theoretical analyses and benchmarks demonstrating the favorability of prefix trees over hash maps for very large state spaces. Additionally, we propose using a Bounded Model Checking (BMC) pre-processing step to impose a variable ordering to further improve memory usage along with preliminary evaluations suggesting its effectiveness. We remark that while our work is motivated primarily by the challenges posed by CRNs, it is generalizable to all CTMC models.

Problem

• Prefix trees reduce memory usage in large-scale CTMC models
• They address hash map limitations for vast state spaces
• The approach is generalizable beyond Chemical Reaction Networks

Innovation

• Prefix trees replace hash maps for memory efficiency
• Bounded Model Checking pre-processing optimizes variable ordering
• Technique generalizes from CRNs to all CTMC models