Technology Category
Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesCognitive Modeling & Cognitive Systems: Symbolic RepresentationsReasoning under Uncertainty: Stochastic Optimization
Prefix Trees Improve Memory Consumption in Large-Scale Continuous-Time Stochastic Models
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
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
Methods, ideas, or system contributions that make the work stand out.
Prefix trees replace hash maps for memory efficiency
Bounded Model Checking pre-processing optimizes variable ordering
Technique generalizes from CRNs to all CTMC models
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