Related papers: General Interpolation and Strong Amalgamation for …
In this paper, the theory of McCarthy's extensional arrays enriched with a maxdiff operation (this operation returns the biggest index where two given arrays differ) is proposed. It is known from the literature that a diff operation is…
The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the…
The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly re-use interpolation…
Training classifiers under fairness constraints such as group fairness, regularizes the disparities of predictions between the groups. Nevertheless, even though the constraints are satisfied during training, they might not generalize at…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
We present an extension to the quantifier-free theory of integer arrays which allows us to express counting. The properties expressible in Array Folds Logic (AFL) include statements such as "the first array cell contains the array length,"…
Existing techniques for Craig interpolation for the quantifier-free fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning $(A, B)$ of the interpolation…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…
Interpolation based software model checkers have been successfully employed to automatically prove programs correct. Their power comes from interpolating SMT solvers that check the feasibility of potential counterexamples and compute…
AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious…
In the past decade the mathematical theory of machine learning has lagged far behind the triumphs of deep neural networks on practical challenges. However, the gap between theory and practice is gradually starting to close. In this paper I…
In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exploited it to handle infinite-state model checking problems. Motivated by applications to the verification of data-aware processes, we proved in a previous paper that…
Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and…
Arrays are commonly used in a variety of software to store and process data in loops. Automatically proving safety properties of such programs that manipulate arrays is challenging. We present a novel verification technique, called…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
We present a novel programming language design that attempts to combine the clarity and safety of high-level functional languages with the efficiency and parallelism of low-level numerical languages. We treat arrays as eagerly-memoized…
We consider the problem of identity testing and recovering (that is, interpolating) of a "hidden" monic polynomials $f$, given an oracle access to $f(x)^e$ for $x\in\mathbb F_q$, where $\mathbb F_q$ is the finite field of $q$ elements and…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinite-state systems. They also help improve the…