# Learning the boundary of inductive invariants

@article{Feldman2021LearningTB, title={Learning the boundary of inductive invariants}, author={Yotam M. Y. Feldman and Shmuel Sagiv and Sharon Shoham and James R. Wilcox}, journal={Proceedings of the ACM on Programming Languages}, year={2021}, volume={5}, pages={1 - 30} }

We study the complexity of invariant inference and its connections to exact concept learning. We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept learning to answer open problems in invariant inference theory. The condition requires the invariant's boundary---the states whose Hamming distance from the invariant is one---to be backwards reachable from the bad states in a small number of steps. Using… Expand

#### 3 Citations

On Symmetry and Quantification: A New Approach to Verify Distributed Protocols

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- NFM
- 2021

This work proposes symmetric incremental induction, an extension of the finite-domain IC3/PDR algorithm, that automatically derives the required quantified inductive invariant by exploiting the connection between symmetry and quantification, and describes a procedure to automatically find a minimal finite size that yields a quantified invariant proving safety for any size. Expand

On Symmetry and Quantification: A New Approach to Verify Distributed Protocols.

- Computer Science
- 2021

This work proposes symmetric incremental induction, an extension of the finite-domain IC3/PDR algorithm, that automatically derives the required quantified inductive invariant by exploiting the connection between symmetry and quantification, and describes a procedure to automatically find a minimal finite size that yields a quantified invariant proving safety for any size. Expand

Property-Directed Reachability as Abstract Interpretation in the Monotone Theory

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- ArXiv
- 2021

This paper shows that, surprisingly, propositional PDR can be formulated as an abstract interpretation algorithm in a logical domain, and defines a version of PDR, called Λ-PDR, in which all generalizations of counterexamples are used to strengthen a frame. Expand

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