Related papers: Interpolation and the Array Property Fragment
The correctness of many algorithms and data structures depends on reachability properties, that is, on the existence of chains of references between objects in the heap. Reasoning about reachability is difficult for two main reasons. First,…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
Different automated theorem provers reason in various deductive systems and, thus, produce proof objects which are in general not compatible. To understand and analyze these objects, one needs to study the corresponding proof theory, and…
Deep neural networks excel at learning the training data, but often provide incorrect and confident predictions when evaluated on slightly different test examples. This includes distribution shifts, outliers, and adversarial examples. To…
A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…
This paper addresses the problem of accurately estimating a function on one domain when only its discrete samples are available on another domain. To answer this challenge, we utilize a neural network, which we train to incorporate prior…
Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general,…
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
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…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
In this paper, we propose new deterministic and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let $f$ be an $n$-variate polynomial given by a straight-line program, which has…
We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…
Bounded Model Checking is one the most successful techniques for finding bugs in program. However, for programs with loops iterating over large-sized arrays, bounded model checkers often exceed the limit of resources available to them. We…
Metamorphic Testing (MT) addresses the test oracle problem by examining the relations between inputs and outputs of test executions. Such relations are known as Metamorphic Relations (MRs). In current practice, identifying and selecting…
We consider the problem of synthesizing provably non-overflowing integer arithmetic expressions or Boolean relations among integer arithmetic expressions. First we use a numerical abstract domain to infer numerical properties among program…
Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…
There is increasing interest in applying verification tools to programs that have bitvector operations. SMT solvers, which serve as a foundation for these tools, have thus increased support for bitvector reasoning through bit-blasting and…
The Split and Rephrase (SPRP) task, which consists in splitting complex sentences into a sequence of shorter grammatical sentences, while preserving the original meaning, can facilitate the processing of complex texts for humans and…
Sparse matrix vector multiplication (SpMV) is a fundamental kernel in scientific codes that rely on iterative solvers. In this first part of our work, we present both a sequential and a basic MPI parallel implementations of SpMV, aiming to…