Monotonicity and the Precision of Program Analysis

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Paper proves that if a program is monotone (non‑decreasing or non‑increasing) on a bounded input space and yields a convex numeric output over a non‑relational domain that refines intervals, then there exists a complete abstract interpretation for that program and those inputs; it formalizes V‑monotonicity with a compositional proof system, gives examples including ReLU neural networks and composed monotone layers, and shows the best correct approximation is complete (existence proof only; termination/widening remains unresolved).

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" chapters (14)

1. 0:00Monotonicity in program analysis
2. 1:49False alarms in analysis
3. 3:12Abstract interpretation assumptions
4. 5:58Completeness rarity in analysis
5. 7:44Program monotonicity role
6. 9:29ReLU monotonicity example
7. 11:19V-monotonicity over variables
8. 13:05Proving monotonicity
9. 14:51V-complete analyzability
10. 15:34Precision and semantics
11. 16:21Q&A: Completeness limits
12. 18:09Q&A: Widening operators
13. 19:34Q&A: Monotone programs
14. 20:41Q&A: Analyzer-program link