Related papers: Performance Analysis of Effective Symbolic Methods…
Lample and Charton (2019) describe a system that uses deep learning technology to compute symbolic, indefinite integrals, and to find symbolic solutions to first- and second-order ordinary differential equations, when the solutions are…
In this work, we propose an automated method to identify semantic bugs in student programs, called ATAS, which builds upon the recent advances in both symbolic execution and active learning. Symbolic execution is a program analysis…
Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments such as Modelica and MapleSim. Before a simulation starts and a numerical solution method is applied, some kind of structural…
We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
This work presents a symbolic approach for estimating the energy consumption for nested loop programs when mapped and scheduled on parallel processor array accelerator architectures. Instead of simulation-based evaluation, we derive a…
This paper presents hep-aid, a modular Python library conceived for utilising, implementing, and developing parameter scan algorithms. Originally devised for sample-efficient, multi-objective active search approaches in computationally…
We propose a novel approach to symbolic timing analysis for digital integrated circuits based on recently developed analytic delay formulas for 2-input NOR, NAND, and Muller-C gates by Ferdowsi et al. (NAHS 2025). Given a fixed order of the…
A new algorithm is derived for computing the actions $f(tA)B$ and $f(tA^{1/2})B$, where $f$ is cosine, sinc, sine, hyperbolic cosine, hyperbolic sinc, or hyperbolic sine function. $A$ is an $n\times n$ matrix and $B$ is $n\times n_0$ with…
Quaternion-valued representations provide a convenient way to model coupled multi-channel signals (e.g., RGB imagery, polarization data, vector fields, and multi-detector time series). Yet practical and numerically reliable software support…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…
The remarkable advancements in artificial intelligence (AI), primarily driven by deep neural networks, are facing challenges surrounding unsustainable computational trajectories, limited robustness, and a lack of explainability. To develop…
We present Ca$\Sigma$oS, the first MATLAB software specifically designed for nonlinear sum-of-squares optimization. A symbolic polynomial algebra system allows to formulate parametrized sum-of-squares optimization problems and facilitates…
Many security and software testing applications require checking whether certain properties of a program hold for any possible usage scenario. For instance, a tool for identifying software vulnerabilities may need to rule out the existence…
The QED-C suite of Application-Oriented Benchmarks provides the ability to gauge performance characteristics of quantum computers as applied to real-world applications. Its benchmark programs sweep over a range of problem sizes and inputs,…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…
These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on…
Conventional tools for formal hardware/software co-verification use bounded model checking techniques to construct a single monolithic propositional formula. Formulas generated in this way are extremely complex and contain a great deal of…