INTERLEAVE: A Faster Symbolic Algorithm for Maximal End Component Decomposition

๐Ÿ“… 2025-05-27
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๐Ÿค– 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 pairsโ€”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 3.81ร— 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.

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๐Ÿ“ 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

Research questions and friction points this paper is trying to address.

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

Methods, ideas, or system contributions that make the work stand out.

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