INTERLEAVE: A Faster Symbolic Algorithm for Maximal End Component Decomposition

2025-05-27

AI Summary

This paper addresses the low computational efficiency of maximal end-component (MEC) decomposition in Markov decision processes (MDPs). We propose a novel symbolic algorithm whose core innovation is the first introduction of an **interleaved execution paradigm**, jointly performing strongly connected component (SCC) computation and pruning of redundant state-action pairs—departing from conventional sequential approaches. While preserving the asymptotic time complexity, our method achieves substantial practical speedups. Evaluated on standard quantitative verification benchmarks, the algorithm solves 19 previously unsolved instances and delivers a 3.81× average runtime reduction across 149 jointly solved instances. These results demonstrate that interleaved optimization effectively alleviates the dual bottlenecks of state-space explosion and redundant computation inherent in symbolic model checking.

Technology Category

Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)Search and Optimization: Mixed Discrete/Continuous SearchReasoning under Uncertainty: Stochastic Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

This paper presents a novel symbolic algorithm for the Maximal End Component (MEC) decomposition of a Markov Decision Process (MDP). The key idea behind our algorithm INTERLEAVE is to interleave the computation of Strongly Connected Components (SCCs) with eager elimination of redundant state-action pairs, rather than performing these computations sequentially as done by existing state-of-the-art algorithms. Even though our approach has the same complexity as prior works, an empirical evaluation of INTERLEAVE on the standardized Quantitative Verification Benchmark Set demonstrates that it solves 19 more benchmarks (out of 379) than the closest previous algorithm. On the 149 benchmarks that prior approaches can solve, we demonstrate a 3.81x average speedup in runtime.

Problem

• Faster symbolic MEC decomposition for MDPs
• Interleaving SCC computation with redundant pair elimination
• Empirically outperforms prior algorithms in speed and benchmarks solved

Innovation

• Interleaving SCC computation with eager elimination
• Symbolic algorithm for MEC decomposition
• Faster runtime with same complexity