# Learning Universally Quantified Invariants of Linear Data Structures

arXiv: https://arxiv.org/abs/1302.2273 · HTML: https://mlsanity.com/paper/1302.2273/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2013.

## Built on by (most cited first, 2 of 2)

- [Leveraging Large Language Models for Automated Proof Synthesis in Rust](https://mlsanity.com/paper/2311.03739/) (2023)
- [Data-driven Verification of Procedural Programs with Integer Arrays](https://mlsanity.com/paper/2505.15958/) (2025)

## Abstract (arXiv)

We propose a new automaton model, called quantified data automata over words, that can model quantified invariants over linear data structures, and build poly-time active learning algorithms for them, where the learner is allowed to query the teacher with membership and equivalence queries. In order to express invariants in decidable logics, we invent a decidable subclass of QDAs, called elastic QDAs, and prove that every QDA has a unique minimally-over-approximating elastic QDA. We then give an application of these theoretically sound and efficient active learning algorithms in a passive learning framework and show that we can efficiently learn quantified linear data structure invariants from samples obtained from dynamic runs for a large class of programs.