Related papers: Tighter Loop Bound Analysis (Technical report)
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
We introduce linear programs encoding regular expressions of finite languages. We show that, given a language, the optimum value of the associated linear program is a lower bound on the size of any regular expression of the language.…
Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…
Recent advancements in tool learning have enabled large language models (LLMs) to integrate external tools, enhancing their task performance by expanding their knowledge boundaries. However, relying on tools often introduces tradeoffs…
Understanding student difficulties in programming is a complex challenge due to the wide range of topics and the abundant varieties of misconceptions and errors. This paper presents the design and development of a fine-grained taxonomy that…
We consider the problem of studying the performance of greedy algorithm on sensor selection problem for stable linear systems with Kalman Filter. Specifically, the objective is to find the system parameters that affects the performance of…
Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…
In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms. The experimental evaluation shows that significant improvements can be made with…
Deadlock detection in recursive programs that admit dynamic resource creation is extremely complex and solutions either give imprecise answers or do not scale. We define an algorithm for detecting deadlocks of "linear recursive programs" of…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of…
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
Optimization seeks extremal points in a function. When there are superextensively many optima, optimization algorithms are liable to get stuck. Under these conditions, generic algorithms tend to find marginal optima, which have many nearly…
When designing an algorithm, one cares about arithmetic/computational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a…
Neural networks are commonly used in safety-critical real-world applications. Unfortunately, the predicted output is often highly sensitive to small, and possibly imperceptible, changes to the input data. Proving that either no such…
Understanding the accuracy limits of machine learning algorithms is essential for data scientists to properly measure performance so they can continually improve their models' predictive capabilities. This study empirically verified the…
Raptor codes have been widely used in many multimedia broadcast/multicast applications. However, our understanding of Raptor codes is still incomplete due to the insufficient amount of theoretical work on the performance analysis of Raptor…
There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops), where questions regarding the runtime and the size…