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Dongsu Kim

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Published work

4 published item(s)

preprint2026arXiv

Sequential Behavioral Watermarking for LLM Agents

LLM-based agents act through sequences of executable decisions, but their trajectories provide little evidence of which agent or policy produced them, making provenance, ownership, and unauthorized reuse difficult to establish from observed behavior alone. This motivates watermarking signals embedded directly into agent behavior rather than only into generated text, since text watermarking cannot capture the action-level decisions that define agent execution. Recent agent watermarking methods address this gap by moving the watermark from generated text to behavioral choices. However, by treating each action step as an independent trial, they overlook trajectory structure and become fragile when trajectories are perturbed, truncated, or observed without reliable alignment. We propose SeqWM, a sequential behavioral watermarking framework that embeds signals into history-conditioned transition patterns and verifies trajectories position-agnostically against random-key baselines. Experiments across diverse agent benchmarks and LLM backbones show that SeqWM consistently achieves reliable detection while preserving agent utility, and remains robust under trajectory corruption where round-indexed behavioral watermarks collapse.

preprint2020arXiv

Refined restricted inversion sequences

Recently, the study of patterns in inversion sequences was initiated by Corteel-Martinez-Savage-Weselcouch and Mansour-Shattuck independently. Motivated by their works and a double Eulerian equidistribution due to Foata (1977), we investigate several classical statistics on restricted inversion sequences that are either known or conjectured to be enumerated by {\em Catalan}, {\em Large Schröder}, {\em Baxter} and {\em Euler} numbers. One of the two highlights of our results is a fascinating bijection between $000$-avoiding inversion sequences and Simsun permutations, which together with Foata's V- and S-codes, provide a proof of a restriced double Eulerian equdistribution. The other one is a refinement of a conjecture due to Martinez and Savage that the cardinality of $\I_n(\geq,\geq,>)$ is the $n$-th Baxter number, which is proved via the so-called {\em obstinate kernel method} developed by Bousquet-Mélou.

preprint2016arXiv

A sextuple equidistribution arising in Pattern Avoidance

We construct an intriguing bijection between $021$-avoiding inversion sequences and $(2413,4213)$-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this result are also presented. Moreover, this result inspires us to characterize all permutation classes that avoid two patterns of length $4$ whose descent polynomial equals that of separable permutations.