arXiv subjects

Xiuwen Yang

Publications and source records attributed to Xiuwen Yang.

5 recordsLinked to original sources

arXiv2026

Assessing the Impact of Requirement Ambiguity on LLM-based Function-Level Code Generation

Software requirement ambiguity is ubiquitous in real-world development, stemming from the inherent imprecision of natural language and the varying interpretations of stakeholders. While Large Language Models (LLMs) have demonstrated impressive capabilities in generating code from precise specifications, such ambiguity poses a significant obstacle to reliable automated code generation. Existing benchmarks typically assume clear and unambiguous requirements, leaving an empirical gap in understanding how LLMs behave when faced with the inherent uncertainty of real-world software requirements. In this paper, we introduce Orchid, the first code generation benchmark specifically designed with ambiguous requirements. It comprises 1,304 function-level tasks covering four distinct types of ambiguity: lexical, syntactic, semantic, and vagueness. Leveraging this dataset, we conduct the first systematic empirical study to evaluate the impact of requirement ambiguity on LLM-based code generation. Our results demonstrate that ambiguity consistently degrades the performance of all evaluated LLMs, with the most pronounced negative effects observed in highly advanced models. Furthermore, we observe that LLMs frequently produce functionally divergent implementations for the same ambiguous requirement and lack the capability to identify or resolve such ambiguity autonomously. These findings reveal a significant performance gap between clear and ambiguous requirements, underscoring the urgent need for ambiguity-aware techniques in the next generation of automated software engineering tools. The Orchid benchmark is publicly available at https://huggingface.co/datasets/SII-YDD/Orchid.

cs.SE↗

arXiv2026

Extremal Laplacian energy of $\overrightarrow{C_{k+1}}$-free digraphs

The Laplacian energy of a digraph $G$ is defined as $\sum_{i=1}^n \lambda_i^2$, where $\lambda_i$ are the eigenvalues of the Laplacian matrix of $G$. A (di)graph $G$ is said to be $H$-free if it does not contain a copy of the fixed (di)graph $H$ as a sub(di)graph. In this paper, we extend the Tur\'{a}n problems to spectral Tur\'{a}n problems in digraphs: what is the maximal Laplacian energy of an $H$-free digraph of given order? In particular, we determine the maximum Laplacian energy and characterize the extremal digraphs of $\overrightarrow{C_{k+1}}$-free digraphs.

math.CO↗

arXiv2023

Sharp bounds for Laplacian spectral moments of digraphs with a fixed dichromatic number

The $k$-th Laplacian spectral moment of a digraph $G$ is defined as $\sum_{i=1}^n λ_i^k$, where $λ_i$ are the eigenvalues of the Laplacian matrix of $G$ and $k$ is a nonnegative integer. For $k=2$, this invariant is better known as the Laplacian energy of $G$. We extend recently published results by characterizing the digraphs which attain the minimal and maximal Laplacian energy within classes of digraphs with a fixed dichromatic number. We also determine sharp bounds for the third Laplacian spectral moment within the special subclass which we define as join digraphs. We leave the full characterization of the extremal digraphs for $k\ge 3$ as an open problem.

math.CO↗

arXiv2021

On the $A_α$ spectral radius and $A_α$ energy of non-strongly connected digraphs

Let $A_α(G)$ be the $A_α$-matrix of a digraph $G$ and $λ_{α1}, λ_{α2}, \ldots, λ_{αn}$ be the eigenvalues of $A_α(G)$. Let $ρ_α(G)$ be the $A_α$ spectral radius of $G$ and $E_α(G)=\sum_{i=1}^n λ_{αi}^2$ be the $A_α$ energy of $G$ by using second spectral moment. Let $\mathcal{G}_n^m$ be the set of non-strongly connected digraphs with order $n$, which contain a unique strong component with order $m$ and some directed trees which are hung on each vertex of the strong component. In this paper, we characterize the digraph which has the maximal $A_α$ spectral radius and the maximal (minimal) $A_α$ energy in $\mathcal{G}_n^m$.

math.CO↗

arXiv2020

Iota energy orderings of bicyclic signed digraphs

The concept of energy of a signed digraph is extended to iota energy of a signed digraph. The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|\text{Re}(z_k)|$, where $\text{Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ vertices, $k=1,2,\ldots,n$. Then the iota energy of $S$ is defined by $E(S)=\sum_{k=1}^n|\text{Im}(z_k)|$, where $\text{Im}(z_k)$ is the imaginary part of eigenvalue $z_k$. In this paper, we consider a special graph class for bicyclic signed digraphs $\mathcal{S}_n$ with $n$ vertices which have two vertex-disjoint signed directed even cycles. We give two iota energy orderings of bicyclic signed digraphs, one is including two positive or two negative directed even cycles, the other is including one positive and one negative directed even cycles.

math.CO↗