### OASIS: ILP-Guided Synthesis of Loop Invariants

Sahil Bhatia,  Saswat Padhi,  Nagarajan Natarajan,  Rahul SharmaPrateek Jain

⟨ In Preparation ⟩

###### Abstract

Finding appropriate inductive loop invariants for a program is a key challenge in verifying its functional properties. Although the problem is undecidable in general, several heuristics have been proposed to handle practical programs that tend to have simple control-flow structures. However, these heuristics only work well when the space of invariants is small. On the other hand, machine-learned techniques that use continuous optimization have a high sample complexity, i.e., the number of invariant guesses and the associated counterexamples, since the invariant is required to exactly satisfy a specification. We propose a novel technique that is able to solve complex verification problems involving programs with larger number of variables and non-linear specifications.

We formulate an invariant as a piecewise low-degree polynomial, and reduce the problem of synthesizing it to a set of integer linear programming (ILP) problems. This enables the use of state-of-the-art ILP techniques that combine enumerative search with continuous optimization; thus ensuring fast convergence for a large class of verification tasks while still ensuring low sample complexity. We instantiate our technique as the open-source Oasis tool using an off-the-shelf ILP solver, and evaluate it on more than $300$ benchmark tasks collected from the annual SyGuS competition and recent prior work. Our experiments show that Oasis outperforms the state-of-the-art tools, including the winner of last year’s SyGuS competition, and is able to solve $9$ challenging tasks that existing tools fail on.

###### BibTeX Citation
@article{corr19/bhatia/oasis,
title         = {OASIS: ILP-Guided Synthesis of Loop Invariants},
author        = {Sahil Bhatia and Saswat Padhi and Nagarajan Natarajan and Rahul Sharma and Prateek Jain},
journal       = {CoRR},
volume        = {abs/1911.11728},
year          = {2019},
eprint        = {1911.11728},
archivePrefix = {arXiv},
primaryClass  = {cs.LG},
url           = {https://arxiv.org/abs/1911.11728}
}