NIL: Learning Nonlinear Interpolants

by   Mingshuai Chen, et al.

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and existing methods have limitations on the form of formulae to be interpolated. We leverage classification techniques with space transformations and kernel tricks as established in the realm of machine learning, and present a counterexample-guided method named NIL for synthesizing polynomial interpolants, thereby yielding a unified framework tackling the interpolation problem for the general quantifier-free theory of nonlinear arithmetic, possibly involving transcendental functions. We prove the soundness of NIL and propose sufficient conditions under which NIL is guaranteed to converge, i.e., the derived sequence of candidate interpolants converges to an actual interpolant, and is complete, namely the algorithm terminates by producing an interpolant if there exists one. The applicability and effectiveness of our technique are demonstrated experimentally on a collection of representative benchmarks from the literature, where in particular, our method suffices to address more interpolation tasks, including those with perturbations in parameters, and in many cases synthesizes simpler interpolants compared with existing approaches.



There are no comments yet.


page 13


Interpolation and Model Checking for Nonlinear Arithmetic

We present a new model-based interpolation procedure for satisfiability ...

When is there a Representer Theorem? Nondifferentiable Regularisers and Banach spaces

We consider a general regularised interpolation problem for learning a p...

AsmetaF: A Flattener for the ASMETA Framework

Abstract State Machines (ASMs) have shown to be a suitable high-level sp...

Neural-Guided Deductive Search for Real-Time Program Synthesis from Examples

Synthesizing user-intended programs from a small number of input-output ...

On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator

We provide a general framework to construct fractal interpolation surfac...

POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systems

We propose POLAR, a polynomial arithmetic framework that leverages polyn...

Harmless interpolation in regression and classification with structured features

Overparametrized neural networks tend to perfectly fit noisy training da...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.