Published April 25, 2026
| Version 1.0
Software
Open
PolyAbs: Parallel Abstract Interpretation for Polynomial Programs with Range Bound Assertions
Authors/Creators
-
1.
Indian Institute of Technology Bombay
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2.
Hong Kong University of Science and Technology
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3.
University of Oxford
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4.
TU Wien
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5.
Singapore Management University
Description
PolyAbs is a static verification tool for polynomial programs based on abstract interpretation. It proves range-bound assertions (e.g., x ∈ [-20, -4] ∪ [4, 20]) by computing over-approximations of reachable states as powersets of hyper-rectangles (boxes). Key technical contributions include novel abstract transformers and refinement operators that more precisely account for the semantics of polynomial assignments and guards, while supporting parallelization and efficient implementation. This is achieved by leveraging Farkas' Lemma and Handelman's Theorem, and by exploiting geometric properties of unions of hyper-rectangles.
The analysis runs in two phases:
- Phase 1 — Widening: computes a sound over-approximation of the reachable set by iterating the transfer functions with widening until a fixpoint is reached.
- Phase 2 — Narrowing: refines the result to reduce over-approximation, improving precision without losing soundness.
Files
cav26-paper211-artifact.zip
Additional details
Software
- Repository URL
- https://github.com/destrat18/PolyAbs.git
- Programming language
- Python
- Development Status
- Concept