arXiv subjects

Sam Urmian

Publications and source records attributed to Sam Urmian.

7 recordsLinked to original sources

arXiv2026

TreeWidzard: An Engine for Width-Based Dynamic Programming and Automated Theorem Proving

In this work, we introduce TreeWidzard, an engine for developing dynamic programming algorithms that decide graph-theoretic properties parameterized by treewidth and pathwidth. Besides providing a unified framework for algorithms deciding atomic graph-theoretic properties, our engine allows one to combine such algorithms for two purposes: to obtain dynamic programming algorithms for more complex graph properties, and to support treewidth-based automated theorem proving. Within this context, given the specification of a Boolean combination $P$ of graph properties $P_1, P_2, \ldots, P_r$, and a positive integer $k$, our engine can be used to determine whether all graphs of treewidth at most $k$ satisfy $P$. The main goal of the present work is to provide a system description of TreeWidzard. In particular, we provide a step-by-step account of how to implement dynamic programming algorithms in our framework and how to combine these algorithms for model checking and automated theorem proving.

cs.DS↗

arXiv2026

State Canonization and Early Pruning in Width-Based Automated Theorem Proving

Width-based automated theorem proving is a framework where counterexamples to graph-theoretic conjectures are searched width-wise relative to some graph width measure, such as treewidth or pathwidth. In a recent work it has been shown that dynamic programming algorithms operating on tree decompositions can be combined together with the purpose of width-based theorem proving. This approach can be used to show that several long-standing conjectures in graph theory can be tested in time $2^{2^{k^{O(1)}}}$ on the class of graphs of treewidth at most $k$. In this work, we give the first steps towards evaluating the viability of this framework from a practical standpoint. At the same time, we advance the framework in two directions. First, we introduce a state-canonization technique that significantly reduces the number of states evaluated during the search for a counterexample of the conjecture. Second, we introduce an early-pruning technique that can be applied in the study of conjectures of the form $\mathcal{P}_1 \rightarrow \mathcal{P}_2$, for graph properties $\mathcal{P}_1$ and $\mathcal{P}_2$, where $\mathcal{P}_1$ is a property closed under subgraphs. As a concrete application, we use our framework in the study of graph-theoretic conjectures related to coloring triangle-free graphs. In particular, our algorithm is able to show that Reed's conjecture for triangle-free graphs is valid on the class of graphs of pathwidth at most 5, and on graphs of treewidth at most 3. Perhaps more interestingly, our algorithm is able to construct in a completely automated way counterexamples to invalid strengthenings of Reed's conjecture. These are the first results showing that width-based automated theorem proving is a promising avenue in the study of graph-theoretic conjectures.

cs.DS↗

arXiv2026

Quality Degradation Attack in Synthetic Data

Synthetic Data Generation (SDG) can be used to facilitate privacy-preserving data sharing. However, most existing research focuses on privacy attacks where the adversary is the recipient of the released synthetic data and attempts to infer sensitive information from it. This study investigates quality degradation attacks initiated by adversaries who possess access to the real dataset or control over the generation process, such as the data owner, the synthetic data provider, or potential intruders. We formalize a corresponding threat model and empirically evaluate the effectiveness of targeted manipulations of real data (e.g., label flipping and feature-importance-based interventions) on the quality of generated synthetic data. The results show that even small perturbations can substantially reduce downstream predictive performance and increase statistical divergence, exposing vulnerabilities within SDG pipelines. This study highlights the need to integrate integrity verification and robustness mechanisms, alongside privacy protection, to ensure the reliability and trustworthiness of synthetic data sharing frameworks.

cs.CR↗

arXiv2025

A Showdown of ChatGPT vs DeepSeek in Solving Programming Tasks

The advancement of large language models (LLMs) has created a competitive landscape for AI-assisted programming tools. This study evaluates two leading models: ChatGPT 03-mini and DeepSeek-R1 on their ability to solve competitive programming tasks from Codeforces. Using 29 programming tasks of three levels of easy, medium, and hard difficulty, we assessed the outcome of both models by their accepted solutions, memory efficiency, and runtime performance. Our results indicate that while both models perform similarly on easy tasks, ChatGPT outperforms DeepSeek-R1 on medium-difficulty tasks, achieving a 54.5% success rate compared to DeepSeek 18.1%. Both models struggled with hard tasks, thus highlighting some ongoing challenges LLMs face in handling highly complex programming problems. These findings highlight key differences in both model capabilities and their computational power, offering valuable insights for developers and researchers working to advance AI-driven programming tools.

cs.SE↗

arXiv2025

Can Synthetic Data be Fair and Private? A Comparative Study of Synthetic Data Generation and Fairness Algorithms

The increasing use of machine learning in learning analytics (LA) has raised significant concerns around algorithmic fairness and privacy. Synthetic data has emerged as a dual-purpose tool, enhancing privacy and improving fairness in LA models. However, prior research suggests an inverse relationship between fairness and privacy, making it challenging to optimize both. This study investigates which synthetic data generators can best balance privacy and fairness, and whether pre-processing fairness algorithms, typically applied to real datasets, are effective on synthetic data. Our results highlight that the DEbiasing CAusal Fairness (DECAF) algorithm achieves the best balance between privacy and fairness. However, DECAF suffers in utility, as reflected in its predictive accuracy. Notably, we found that applying pre-processing fairness algorithms to synthetic data improves fairness even more than when applied to real data. These findings suggest that combining synthetic data generation with fairness pre-processing offers a promising approach to creating fairer LA models.

cs.LG↗

arXiv2025

Creating Artificial Students that Never Existed: Leveraging Large Language Models and CTGANs for Synthetic Data Generation

In this study, we explore the growing potential of AI and deep learning technologies, particularly Generative Adversarial Networks (GANs) and Large Language Models (LLMs), for generating synthetic tabular data. Access to quality students data is critical for advancing learning analytics, but privacy concerns and stricter data protection regulations worldwide limit their availability and usage. Synthetic data offers a promising alternative. We investigate whether synthetic data can be leveraged to create artificial students for serving learning analytics models. Using the popular GAN model CTGAN and three LLMs- GPT2, DistilGPT2, and DialoGPT, we generate synthetic tabular student data. Our results demonstrate the strong potential of these methods to produce high-quality synthetic datasets that resemble real students data. To validate our findings, we apply a comprehensive set of utility evaluation metrics to assess the statistical and predictive performance of the synthetic data and compare the different generator models used, specially the performance of LLMs. Our study aims to provide the learning analytics community with valuable insights into the use of synthetic data, laying the groundwork for expanding the field methodological toolbox with new innovative approaches for learning analytics data generation.

cs.LG↗

arXiv2022

From Width-Based Model Checking to Width-Based Automated Theorem Proving

In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we introduce a general framework to convert a large class of width-based model-checking algorithms into algorithms that can be used to test the validity of graph-theoretic conjectures on classes of graphs of bounded width. Our framework is modular and can be applied with respect to several well-studied width measures for graphs, including treewidth and cliquewidth. As a quantitative application of our framework, we prove analytically that for several long-standing graph-theoretic conjectures, there exists an algorithm that takes a number $k$ as input and correctly determines in time double-exponential in $k^{O(1)}$ whether the conjecture is valid on all graphs of treewidth at most $k$. These upper bounds, which may be regarded as upper-bounds on the size of proofs/disproofs for these conjectures on the class of graphs of treewidth at most $k$, improve significantly on theoretical upper bounds obtained using previously available techniques.

cs.DS↗