Learning Canonical Register Automata over Ordered Data Domains

Register automata are finite automata equipped with memory that recognize data languages over infinite alphabets. In this work, we investigate active learning algorithms for deterministic register automata (DRAs) over ordered data domains--covering both dense domains, such as the rationals, and non-dense domains such as the integers. We show that the active learning problem for DRAs over both dense and non-dense ordered domains can be treated within a single unified framework. More specifically, we develop and implement a polynomial-time active learning procedure for DRAs over ordered domains, using oracles for membership, equivalence and memorability queries. The memorability queries were originally introduced for learning DRAs over domains with identity tests. Our unified framework also leads to a new consequence: minimization of DRAs over the non-dense ordered domain of integers is decidable, extending a result previously known only for dense domains. Finally, we give improved complexity bounds of several decision problems for DRAs over ordered domains that are closely related to the queries used in active learning.

Playing ZendoWorld: Challenging AI Agents on Active Visual Concept Induction

A central challenge in building intelligent systems is enabling agents to jointly perceive complex inputs, form hypotheses about hidden patterns, and design informative experiments to test them. To study this problem, we propose ZendoWorld, a controlled interactive environment in which agents must infer a logical rule about visual game observations, acquire information by proposing new scenes, and refine their hypotheses based on feedback from the game environment. We evaluate several agents spanning pure VLM reasoning, Bayesian particle filtering, dynamic concept discovery, and neuro-symbolic methods. Our main findings are: (1) high accuracy in predicting labels for observed examples does not imply recovery of the underlying rule; (2) perception and induction are distinct bottlenecks for different agent classes; and (3) VLM-based agents propose near-uninformative experiments, failing to actively reduce hypothesis uncertainty. To compare these results, we collect human data on the task, which reveals a gap in inductive reasoning, particularly for more complex rules. Overall, ZENDOWORLD takes an important step toward evaluating intelligent agents and identifies concrete avenues for improvement, particularly in domains like scientific discovery.