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About this paper
Chenyu Zhou, Di Wang, Thomas Reps
A compositional analysis framework, Dickens, computes moments of probabilistic program costs, including non-linear max and min operators, using prefix-tail surrogate distributions with sound error bounds. The system showed improved accuracy and robust performance compared to prior approximations in benchmarks like quantum repeater waiting times and RFID collision resolution.
Key insights
- Capturing distributional shape information, not just scalar moments, is crucial for soundly analyzing probabilistic costs involving non-linear operators like max and min, which is achieved by the prefix-tail surrogate distributions.
- Error propagation must differentiate between distributional shape error (which drives moment error in non-linear operations) and direct moment error, with operator-specific contracts determining how these errors combine and amplify.
- The analysis precision is systematically tunable through configurable prefix depth and the strategic promotion of subexpressions to exact oracles, guided by an error attribution mechanism to target high-impact error sources.
Summary by alphaXiv.
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