Related papers: An Algorithm for Verifying Some Norm Identities in…
We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…
In this article we address the problem of automatic answer checking in interactive learning systems that support mathematical notation. This problem consists of the problem of establishing identities in formal mathematical systems and hence…
Generating confidence calibrated outputs is of utmost importance for the applications of deep neural networks in safety-critical decision-making systems. The output of a neural network is a probability distribution where the scores are…
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…
The Verified Software Toolchain (VST) is a system for proving correctness of C programs using separation logic. By connecting to the verified compiler CompCert, it produces the strongest possible guarantees of correctness for real C code…
Verification of algorithms and data structures utilized in modern autonomous and semi-autonomous vehicles for land, sea, air, and space presents a significant challenge. Autonomy algorithms, e.g., route planning, pattern matching, and…
We present a novel framework for specifying and verifying correctness globally for neural networks on perception tasks. Most previous works on neural network verification for perception tasks focus on robustness verification. Unlike…
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
Current approaches to neural network verification focus on specifications that target small regions around known input data points, such as local robustness. Thus, using these approaches, we can not obtain guarantees for inputs that are not…
Let $\xi$ be a random integer vector, having uniform distribution \[\mathbf{P} \{\xi = (i_1,i_2,...,i_n) = 1/n^n \} \ \hbox{for} \ 1 \leq i_1,i_2,...,i_n\leq n.\] A realization $(i_1,i_2,...,i_n)$ of $\xi$ is called \textit{good}, if its…
This paper presents both a proof method and a result. The proof method presented is particularly suitable for uniformly proving families of identities satisfied by a family of recursive sequences. To illustrate the method, we study the…
Recent developments in Large Language Models (LLMs) have shown promise in automating code generation, yet the generated programs lack rigorous correctness guarantees. Formal verification can address this shortcoming, but requires expertise…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
A finite-dimensional normed space is an inner product space if and only if the set of norming vectors of any endomorphism is a linear subspace. This theorem was proved by Sain and Paul for real scalars. In this paper, we give a different…
2LS ("tools") is a verification tool for C programs, built upon the CPROVER framework. It allows one to verify user-specified assertions, memory safety properties (e.g. buffer overflows), numerical overflows, division by zero, memory leaks,…
The No Free Lunch theorems prove that under a uniform distribution over induction problems (search problems or learning problems), all induction algorithms perform equally. As I discuss in this chapter, the importance of the theorems arises…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
Results of neural network learning are always subject to some variability, due to the sensitivity to initial conditions, to convergence to local minima, and, sometimes more dramatically, to sampling variability. This paper presents a set of…
This paper proposes a technique to specify and verify whether a loop can be parallelised. Our approach can be used as an additional step in a parallelising compiler to verify user annotations about loop dependences. Essentially, our…
Internal cluster validity measures (such as the Calinski-Harabasz, Dunn, or Davies-Bouldin indices) are frequently used for selecting the appropriate number of partitions a dataset should be split into. In this paper we consider what…