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Zhenbang Chen

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4 papers

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FM Conference 2026 Conference Paper

EUF-based Solving Dyck-Reachability with Applications to Static Analysis

Yide Du
Zhenbang Chen
Kunlin Liu
Guofeng Zhang
Xudong Wang
Ke Ma
Wei Dong
Ji Wang

Abstract Static analysis plays a crucial role in program optimization, bug detection, and automated testing. Dyck-reachability provides a foundational formulation for static analysis, as Dyck grammars can model critical properties such as field and context sensitivity, thus offering broad applicability. This paper shows that static analysis problems modeled as Dyck-reachability on bidirected graphs can be encoded into the EUF SMT theory; consequently, all such problems admit efficient formulation and solution via EUF-based SMT solvers. By leveraging the optimized nature of modern SMT solvers, our method achieves efficiency comparable to state-of-the-art graph-based bidirected Dyck-reachability algorithms while eliminating the need for developing complex specialized graph reachability algorithms. Our approach opens new avenues for solving these classical static analysis problems, demonstrating the strong potential of SMT solvers in encoding static analysis solutions.

DOI

FM Conference 2026 Conference Paper

Selective Concolic Testing

Guofeng Zhang
Zhenbang Chen
Ziqi Shuai
Jun Sun
Weijiang Hong
Yufeng Zhang
Ji Wang
Yang Liu

Abstract The principled combination of symbolic execution and random testing lacks a formal foundation, especially in deciding which inputs to symbolize. We propose selective concolic testing, a cost-aware framework that formulates this choice as an optimized policy problem of a MDP (Markov Decision Process). We model program exploration over a finite control-flow graph, where MDP states represent covered statements, actions partition path constraints into symbolic and random fragments, rewards reflect coverage gain, and costs account for SMT solving effort and sampling inefficiency. Our framework yields the first formal characterization of selective symbolization as policy synthesis in a probabilistic system. We prove that exact policy computation is intractable due to the exponential state space and the hardness of solution-density estimation via model counting. Our formulation enables a practical approximation: we partition constraint dependency graphs and use machine learning to predict solver timeouts, guiding per-constraint symbolization decisions. Built on top of KLEE and JFS, our prototype validates the approach on real-world floating-point benchmarks. Results show that selectively symbolizing inputs, guided by predicted solvability and cost, significantly improves coverage efficiency. Our work thus provides both a rigorous theoretical foundation and a practical instantiation for hybrid program analysis.

DOI

NeurIPS Conference 2023 Conference Paper

On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions

Yufeng Zhang
Jialu Pan
Li Ken Li
Wanwei Liu
Zhenbang Chen
Xinwang Liu
J Wang

Kullback-Leibler (KL) divergence is one of the most important measures to calculate the difference between probability distributions. In this paper, we theoretically study several properties of KL divergence between multivariate Gaussian distributions. Firstly, for any two $n$-dimensional Gaussian distributions $\mathcal{N}_1$ and $\mathcal{N}_2$, we prove that when $KL(\mathcal{N}_2||\mathcal{N}_1)\leq \varepsilon\ (\varepsilon>0)$ the supremum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ is $(1/2)\left((-W_{0}(-e^{-(1+2\varepsilon)}))^{-1}+\log(-W_{0}(-e^{-(1+2\varepsilon)})) -1 \right)$, where $W_0$ is the principal branch of Lambert $W$ function. For small $\varepsilon$, the supremum is $\varepsilon + 2\varepsilon^{1. 5} + O(\varepsilon^2)$. This quantifies the approximate symmetry of small KL divergence between Gaussian distributions. We further derive the infimum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ when $KL(\mathcal{N}_2||\mathcal{N}_1)\geq M\ (M>0)$. We give the conditions when the supremum and infimum can be attained. Secondly, for any three $n$-dimensional Gaussian distributions $\mathcal{N}_1$, $\mathcal{N}_2$, and $\mathcal{N}_3$, we theoretically show that an upper bound of $KL(\mathcal{N}_1||\mathcal{N}_3)$ is $3\varepsilon_1+3\varepsilon_2+2\sqrt{\varepsilon_1\varepsilon_2}+o(\varepsilon_1)+o(\varepsilon_2)$ when $KL(\mathcal{N}_1||\mathcal{N}_2)\leq \varepsilon_1$ and $KL(\mathcal{N}_2||\mathcal{N}_3)\leq \varepsilon_2$ ($\varepsilon_1, \varepsilon_2\ge 0$). This reveals that KL divergence between Gaussian distributions follows a relaxed triangle inequality. Note that, all these bounds in the theorems presented in this work are independent of the dimension $n$. Finally, we discuss several applications of our theories in deep learning, reinforcement learning, and sample complexity research.

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TCS Journal 2012 Journal Article

Failure-divergence semantics and refinement of long running transactions

Zhenbang Chen
Zhiming Liu
Ji Wang

Compensating CSP (cCSP) models long-running transactions. It can be used to specify service orchestrations written in programming languages like WS-BPEL. However, the original cCSP does not allow to model internal (non-deterministic) choice, synchronized parallel composition, hiding or recursion. In this paper, we introduce these operators and define for the extended language a failure-divergence (FD) semantics to allow reasoning about non-determinism, deadlock and livelock. Furthermore, we develop a refinement calculus that allows us to compare the level of non-determinism between long running transactions, and transform specifications for design and analysis.

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