Related papers: The Liouville Generator for Producing Integrable E…
Generating code from natural-language requirements has become a primary route for LLM-assisted software development. Although LLMs can successfully complete small programming tasks, generating an entire complex project remains unreliable…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
In this paper we will present SDeval, a software project that contains tools for creating and running benchmarks with a focus on problems in computer algebra. It is built on top of the Symbolic Data project, able to translate problems in…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Data augmentation is a powerful mechanism in equivariant machine learning, encouraging symmetry by training networks to produce consistent outputs under transformed inputs. Yet, effective augmentation typically requires the underlying…
Generating diverse, readable statistical charts from tabular data remains challenging for LLMs, as many failures become apparent after rendering and are not detectable from data or code alone. Existing chart datasets also rarely provide…
An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…
Artistic Glyph Image Generation (AGIG) differs from current creativity-focused generation models by offering finely controllable deterministic generation. It transfers the style of a reference image to a source while preserving its content.…
How humans can effectively and efficiently acquire images has always been a perennial question. A classic solution is text-to-image retrieval from an existing database; however, the limited database typically lacks creativity. By contrast,…
Prior methods for controlling image generation are limited in their ability to be taught new tasks. In contrast, vision-language models, or VLMs, can learn tasks in-context and produce the correct outputs for a given input. We propose a…
Recent advancements in image synthesis are fueled by the advent of large-scale diffusion models. Yet, integrating realistic object visualizations seamlessly into new or existing backgrounds without extensive training remains a challenge.…
Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…
Large Language Models (LLMs) have shown potential for solving mathematical tasks. We show that LLMs can be utilized to generate proofs by induction for hardware verification and thereby replace some of the manual work done by Formal…
It is shown that a linear separation relations are fundamental objects for integration by quadratures of St\"{a}ckel separable Liouville integrable systems (the so-called St\"{a}ckel systems). These relations are further employed for the…
The integration of large language models (LLMs) into robotic systems has accelerated progress in embodied artificial intelligence, yet current approaches remain constrained by existing robotic architectures, particularly serial mechanisms.…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
Generating accurate and consistent visual aids is a critical challenge in mathematics education, where visual representations like geometric shapes and functions play a pivotal role in enhancing student comprehension. This paper introduces…
We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…
This article discusses a new technique to automatically generate test cases for object oriented programs. At the state of the art, the problem of generating adequate sets of complete test cases has not been satisfactorily solved yet. There…