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Hengbin Zhang

Publications and source records attributed to Hengbin Zhang.

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Sharpen the Spec, Cut the Code: A Case for Generative File System with SYSSPEC

File systems are critical OS components that require constant evolution to support new hardware and emerging application needs. However, the traditional paradigm of developing features, fixing bugs, and maintaining the system incurs significant overhead, especially as systems grow in complexity. This paper proposes a new paradigm, generative file systems, which leverages Large Language Models (LLMs) to generate and evolve a file system from prompts, effectively addressing the need for robust evolution. Despite the widespread success of LLMs in code generation, attempts to create a functional file system have thus far been unsuccessful, mainly due to the ambiguity of natural language prompts. This paper introduces SYSSPEC, a framework for developing generative file systems. Its key insight is to replace ambiguous natural language with principles adapted from formal methods. Instead of imprecise prompts, SYSSPEC employs a multi-part specification that accurately describes a file system's functionality, modularity, and concurrency. The specification acts as an unambiguous blueprint, guiding LLMs to generate expected code flexibly. To manage evolution, we develop a DAG-structured patch that operates on the specification itself, enabling new features to be added without violating existing invariants. Moreover, the SYSSPEC toolchain features a set of LLM-based agents with mechanisms to mitigate hallucination during construction and evolution. We demonstrate our approach by generating SPECFS, a concurrent file system. SPECFS demonstrates equivalent level of correctness to that of a manually-coded baseline across hundreds of regression tests. We further confirm its evolvability by seamlessly integrating 10 real-world features from Ext4. Our work shows that a specification-guided approach makes generating and evolving complex systems not only feasible but also highly effective.

cs.OS

Symplectic inner product graphs and their automorphisms

A new graph, called the symplectic inner product graph $Spi\big(2ν,q\big)$, over a finite field $\mathbb{F}_q$ is introduced. We show that $Spi\big(2ν,q\big)$ is connected with diameter $4$ if and only if $ν\geq2$ and the automorphism group of $Spi\big(2ν,q\big)$ is determined. Two necessary and sufficient conditions for two vertices of $Spi\big(2ν,q\big)$ and two edges of $Spi\big(2ν,q\big)$ respectively are in the same orbit under the action of the automorphism group of $Spi\big(2ν,q\big)$ are obtained.

math.CO

Orthogonal inner product graphs of odd characteristic and their automorphisms

Let $\mathbb{F}_q$ be a finite field of odd characteristic and $2ν+δ\geq2$ an integer number with $δ=0,1$ or $2$. The orthogonal inner product graph $Oi\big(2ν+δ,q\big)$ over $\mathbb{F}_q$ is defined and the automorphism groups of $Oi\big(2ν+δ,q\big)$ are determined. We show that $Oi\big(2ν+δ,q\big)$ is a disconnected graph if $2ν+δ=2$; otherwise it is not. Moreover, we have two necessary and sufficient conditions for two vertices of $Oi\big(2ν+δ,q\big)$ and two edges of $Oi\big(2ν+δ,q\big)$ respectively are in the same orbit under the action of the automorphism group of $Oi\big(2ν+δ,q\big).$

math.CO

A note on the zero divisor graph of the ring of Lipschitz integers modulo $n$

In a recent paper, Grau et al. (2017) studied the zero divisor graphs of the ring of Lipschitz integers modulo $n$, and computed the domination number of the undirected zero divisor graph of the ring of Lipschitz integers modulo $n$. But the case $n$ is a power of prime numbers remained open. In this note, this problem is solved. We also show the automorphism group of the zero divisor graph of the ring of Lipschitz integers modulo $2^s$.

math.CO

Modeling Multi-wavelength Pulse Profiles of Millisecond Pulsar PSR B1821-24

PSR B1821$-$24 is a solitary millisecond pulsar (MSP) which radiates multi-wavelength pulsed photons. It has complex radio, X-ray and $γ$-ray pulse profiles with distinct peak phase-separations that challenge the traditional caustic emission models. Using the single-pole annular gap model with suitable magnetic inclination angle ($α=40^\circ$) and viewing angle ($ζ=75^\circ$), we managed to reproduce its pulse profiles of three wavebands. It is found that the middle radio peak is originated from the core gap region at high altitudes, and the other two radio peaks are originated from the annular gap region at relatively low altitudes. Two peaks of both X-ray and $γ$-ray wavebands are fundamentally originated from annular gap region, while the $γ$-ray emission generated from the core gap region contributes somewhat to the first $γ$-ray peak. Precisely reproducing the multi-wavelength pulse profiles of PSR B1821$-$24 enables us to understand emission regions of distinct wavebands and justify pulsar emission models.

astro-ph.SR