Selected work

Representative Papers

On the Decidability of Monadic Second-Order Logic with Arithmetic Predicates

May 13, 2024Logic in Computer Science

This work addresses the decidability of monadic second-order (MSO) logic over the natural number structure ⟨ℕ; <, P₁,…,P_d⟩, where each P_i is a canonical arithmetic predicate (e.g., powers of k, perfect k-th powers ℕ^k, or the Fibonacci sequence Fib). We develop an interdisciplinary decidability framework integrating symbolic dynamical systems, transcendental number theory (including the Schanuel Conjecture), finite automata theory, and logical analysis. Unconditionally—i.e., without unproven hypotheses—we establish MSO decidability for key structures such as (ℕ; <, Pow2, Fib) and (ℕ; <, Pow2, Pow3, Pow6). We further prove Turing equivalence between the MSO theory of (ℕ; <, Pow2, ℕ²) and that of binary normal numbers. Crucially, our approach uncovers deep connections between combinatorial encoding properties of arithmetic predicates and their representability by finite automata, yielding a systematic methodological advance for decidability research at the interface of logic and number theory.

7 citations1 influentialRead paper

Balanced-chromatic number and Hadwiger-like conjectures

Aug 02, 2023arXiv.org

This work addresses the extension of Hadwiger’s conjecture to signed graphs. It introduces the *balanced chromatic number*—the minimum number of vertex subsets required such that no subset induces a negative cycle—as the central combinatorial tool. By establishing a quantitative relationship between the balanced chromatic number and the existence of a ( ilde{K}_t) subdivision, the authors prove an upper bound of (O(t^2)), specifically (frac{79}{2}t^2). They formulate and rigorously prove the *signed-graph analogue of Hadwiger’s conjecture*, demonstrating its equivalence to the classical conjecture. Furthermore, they generalize Kawarabayashi’s result on odd minors to the signed-graph setting and uncover a deep connection between the balanced chromatic number and the odd Hadwiger conjecture. The work unifies structural coloring, minor theory, and subdivision analysis for signed graphs, providing a novel framework for Hadwiger-type problems in signed graph theory.

6 citationsRead paper

Mirroring Call-by-Need, or Values Acting Silly

Feb 19, 2024International Conference on Formal Structures for Computation and Deduction

This paper addresses the compositional interaction of copying and erasing behaviors in λ-calculus, identifying a gap in understanding how inefficiencies in evaluation strategies arise from their interplay. Method: We introduce *call-by-silly*, a symmetrically degenerate evaluation strategy orthogonal to call-by-need, deliberately combining the redundant copying of call-by-name with the blind erasure of call-by-value. We formally define the call-by-silly calculus and—using rewriting theory and a tight multi-type system—rigorously prove its contextual equivalence to call-by-value. Moreover, we construct the first type system that precisely characterizes the length of longest reduction sequences. Contribution: Our work reveals that contextual equivalence is insensitive to operational inefficiencies; provides the first symmetric degenerate model exhibiting both worst-case copying and worst-case erasure; and achieves a decidable, type-based characterization of evaluation length—establishing a novel bridge between type-theoretic precision and quantitative operational semantics.

3 citationsRead paper

Explorable Parity Automata

Oct 30, 2024arXiv.org

This paper addresses the problem of nondeterminism resolution over both finite and infinite words, generalizing history-deterministic (HD) automata. It introduces *explorable automata*—a novel paradigm formalized for the first time—as a unifying framework encompassing both finite-word (explorable) and infinite-word (ω-explorable) settings. The method establishes polynomial-time equivalences between explorable/ω-explorable automata and HD automata. For parity, safety, and coBüchi acceptance conditions, it fully characterizes the computational complexity of deciding explorability as ExpTime-complete, and shows that HD parity automata with fixed index are recognizable in PTime. Furthermore, it precisely delineates the expressive power of explorable automata within the parity index hierarchy. Integrating automata theory, game semantics, and complexity analysis, this work provides a more general and principled modeling framework for controlled nondeterminism.

2 citationsRead paper

Parameterized Spanning Tree Congestion

Oct 10, 2024International Symposium on Mathematical Foundations of Computer Science

This paper studies the Tree Congestion Minimization problem: given a graph (G = (V,E)), compute a spanning tree (T) minimizing the maximum number of vertex-pair unique paths in (T) traversing any single edge—i.e., the edge congestion. While known to be NP-hard, its parameterized complexity remained open for years. We resolve this by proving, under the Exponential Time Hypothesis (ETH), that the problem is not fixed-parameter tractable (FPT) with respect to treewidth. Using a novel generic reduction framework, we establish W[1]-hardness with respect to stronger or incomparable structural parameters—including tree-depth plus feedback vertex set, and twin cover. Furthermore, we show NP-completeness even on graphs with maximum degree (Delta = 8) and modular width (mathrm{mw} = 4). These results comprehensively settle multiple long-standing open questions and significantly advance the theoretical boundaries of structural parameterized algorithms.

2 citationsRead paper

Recent publications

Latest Papers

Mastering Stochastic OLG Models in Continuous Time

Aug 11, 2026

This study addresses the challenge of computing equilibria in continuous-time overlapping generations (OLG) models featuring both idiosyncratic and aggregate risks. To this end, it introduces a novel “finite-difference neural operator” method that formulates equilibrium via a master equation, representing the joint distribution over continuous age, wealth, and individual states through a support function fed into a neural network, which then outputs a finite-difference representation of the conditional value function. By integrating the high-dimensional approximation capacity of neural networks with the finite-difference method’s precise handling of boundary conditions and economic shape constraints, the approach establishes a mesh-free framework for solving high-dimensional distributional equilibria. The method is applied to two OLG settings—one with only aggregate risk and another incorporating both idiosyncratic and aggregate risks—demonstrating its flexibility, accuracy, and scalability.

0 citationsRead paper

leaspy: LEArning Spatiotemporal Patterns in PYthon

Aug 10, 2026

This work addresses the challenge of temporal misalignment in longitudinal data arising from inter-individual differences in the onset and progression rates of dynamic processes. To this end, the authors introduce leaspy, an open-source Python library based on mixed-effects models. The framework enables multivariate modeling of continuous, time-to-event, and mixed data types within a unified formulation, facilitating both population-level trajectory estimation and individual-specific deviation capture. A dedicated time-warping algorithm is incorporated to align heterogeneous longitudinal observations across subjects. Notably, this is the first implementation to integrate multivariate heterogeneous longitudinal modeling in a scalable and robust software architecture. The method has been successfully applied in neurodegenerative disease research, where it effectively characterizes disease heterogeneity and yields accurate personalized predictions, demonstrating its practical utility and validity.

0 citationsRead paper

TCS-BENCH: Benchmarking State-of-the-Art Generative AI Theoretical Computer Science Research Ability

Aug 10, 2026

This work addresses the lack of systematic evaluation benchmarks for assessing large language models’ ability to generate research-level theorem proofs in theoretical computer science (TCS). It introduces TCS-Bench, the first structured benchmark specifically designed for proof generation of theorems drawn from top-tier conference papers in STOC, FOCS, and SODA. To support self-contained proof synthesis, the benchmark adopts a context-augmented task formulation. A key contribution is the development of a high-precision automated verification agent, which achieves over 90% accuracy on expert-annotated data and effectively aligns with human judgment. This framework provides a reliable and scalable foundation for evaluating the reasoning and formal proof capabilities of generative AI systems in theoretical computer science.

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Evaluating the influence of treatment-effect heterogeneity on discrimination

Aug 06, 2026

This study addresses the limited understanding of how well conditional average treatment effect (CATE) models can discriminate heterogeneous treatment effects across subpopulations. The authors construct 20 theoretical outcome distributions varying in both average treatment effect and heterogeneity levels, and systematically evaluate the performance of three discrimination metrics—benefit c-statistic, benefit concentration, and PAPE—under ideal CATE assumptions. Their analysis reveals marked differences in the metrics’ dependence on treatment effect heterogeneity: benefit concentration achieves perfect discrimination even under minimal heterogeneity, whereas high values of the c-statistic and PAPE require substantially stronger heterogeneity. These findings challenge the common practice of relying on a single metric to assess CATE model performance and underscore the sensitivity of metric selection to the underlying degree of treatment effect heterogeneity.

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PPDL: LLM-Based Flows as Probabilistic Programs

Aug 05, 2026

This work addresses the challenge of unreliable confidence quantification in multi-step large language model (LLM) pipelines, which undermines result trustworthiness and hampers debugging. The authors propose a novel probabilistic programming language that formalizes LLM invocation workflows as probabilistic programs, enabling automatic tracking and propagation of uncertainty throughout the entire pipeline. This framework supports flexible experimentation with diverse inference-time scaling strategies without requiring additional code. The approach substantially enhances system reliability and debuggability, and empirical evaluations demonstrate its effectiveness in accurately quantifying uncertainty. As a practical application, the method successfully powers an automated theorem-proving agent integrated with the Rocq theorem prover.

0 citationsRead paper