## Abstract

We address the problem of computing an abstraction for a set of examples, which is precise enough to separate them from a set of counterexamples. The challenge is to find an over-approximation of the positive examples that does not represent any negative example. Conjunctive abstractions (e.g., convex numerical domains) and limited disjunctive abstractions, are often insufficient, as even the best such abstraction might include negative examples. One way to improve precision is to consider a general disjunctive abstraction. We present D^{3}, a new algorithm for learning general disjunctive abstractions. Our algorithm is inspired by widely used machine-learning algorithms for obtaining a classifier from positive and negative examples. In contrast to these algorithms which cannot generalize from disjunctions, D^{3} obtains a disjunctive abstraction that minimizes the number of disjunctions. The result generalizes the positive examples as much as possible without representing any of the negative examples. We demonstrate the value of our algorithm by applying it to the problem of data- driven differential analysis, computing the abstract semantic difference between two programs. Our evaluation shows that D^{3} can be used to effectively learn precise differences between programs even when the difference requires a disjunctive representation.

Original language | English |
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Title of host publication | Verification, Model Checking, and Abstract Interpretation - 17th International Conference, VMCAI 2016, Proceedings |

Editors | K. Rustan, M. Leino, Barbara Jobstmann |

Publisher | Springer Verlag |

Pages | 185-205 |

Number of pages | 21 |

ISBN (Print) | 9783662491218 |

DOIs | |

State | Published - 2016 |

Externally published | Yes |

Event | 17th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2016 - St. Petersburg, United States Duration: 17 Jan 2016 → 19 Jan 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9583 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 17th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2016 |
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Country/Territory | United States |

City | St. Petersburg |

Period | 17/01/16 → 19/01/16 |

### Funding

Funders | Funder number |
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Seventh Framework Programme | 615688 |

European Commission | 321174-VSSC |

United States-Israel Binational Science Foundation | 2012259 |

Seventh Framework Programme |

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