Many AI-based code assistants, particularly those powered by Large Language Models (LLMs), provide complete solutions, which can reduce active problem solving and limit incidental learning, the acquisition of knowledge as a byproduct of task engagement. Such learning requires active participation rather than passive acceptance of AI-generated answers, which might be incorrect. This study examines how incidental learning can be supported through guided interaction. We present LeetCoach, an LLM-assisted coding platform that applies a cognitive forcing strategy, prompting learners to reflect and take incremental steps instead of receiving full solutions. Using LeetCode-style questions, we conducted a pilot study with novice and advanced college programmers who completed tasks under assisted and unassisted conditions. Novices showed substantial post-test gains despite receiving AI guidance only during the intervention, suggesting that incidental exposure improved later performance. Advanced learners showed smaller gains. Across both groups, participants required fewer debugging attempts in the post-test compared to earlier stages, indicating improved debugging efficiency and algorithmic understanding. These findings provide early evidence that LLMs can be designed to promote indirect learning while shaping problem-solving strategies. This work offers a proof of concept for cognitively informed tutoring systems in computer science education and discusses implications for integrating LLMs to enhance both immediate outcomes and lasting skill development.

The multi-robot visibility-based pursuit-evasion problem tasks a team of robots with systematically searching an environment to detect (capture) an evader. Previous techniques to generate search strategies for the pursuit team have shown to be either computationally intractable or permit poor solution quality. This paper presents a novel asymptotically optimal algorithm for generating a joint motion strategy for the pursuers. To explore the space of possible pursuer motion strategies, the algorithm utilizes a trio of hierarchical graph data structures that each capture certain elements of the problem such as connectivity (valid single pursuer motion), coordination (multiple pursuer motion), and tracking information (evaluating where an evader may be). The algorithm is inspired by well-known methods in the motion planning literature and inherits its asymptotic optimality from those techniques. In addition, we describe a method that can improve upon solutions found during the formative stages of the main algorithm, using a "fast-forward" approach that foregoes guarantees of asymptotic optimality, implementing heuristics that concentrate future samples into improving the path quality of the nominal solution. The algorithms were validated in simulation and results are provided.

This paper studies a multi-robot visibility-based pursuit-evasion problem in which a group of pursuer robots are tasked with detecting an evader within a two dimensional polygonal environment. The primary contribution is a novel formulation of the pursuit-evasion problem that modifies the pursuers' objective by requiring that the evader still be de-tected, even in spite of the failure of any single pursuer robot. This novel constraint, whereby two pursuers are required to detect an evader, has the benefit of providing redundancy to the search, should any member of the team become unresponsive, suffer temporary sensor disruption/failure, or otherwise become incapacitated. Existing methods, even those that are designed to respond to failures, rely on the pursuers to replan and update their search pattern to handle such occurrences. In contrast, the proposed formulation produces plans that are inherently tolerant of some level of disturbance. Building upon this new formulation, we introduce an augmented data structure for encoding the problem state and a novel sampling technique to ensure that the generated plans are robust to failures of any single pursuer robot. An implementation and simulation results illustrating the effectiveness of this approach are described.

Given a two-dimensional polygonal space, the multi-robot visibility-based pursuit-evasion problem tasks several pursuer robots with the goal of establishing visibility with an arbitrarily fast evader. The best known complete algorithm for this problem takes time doubly exponential in the number of robots. However, sampling-based techniques have shown promise in generating feasible solutions in these scenarios. One of the primary drawbacks to employing existing sampling-based methods is that existing algorithms have long execution times and high failure rates for complex environments. This paper addresses that limitation by proposing a new algorithm that takes an environment as its input and returns a joint motion strategy which ensures that the evader is captured by one of the pursuers. Starting with a single pursuer, we sequentially construct Sample-Generated Pursuit-Evasion Graphs to create such a joint motion strategy. This sequential graph structure ensures that our algorithm will always terminate with a solution, regardless of the complexity of the environment. We describe an implementation of this algorithm and present quantitative results that show significant improvement in comparison to the existing algorithm.

This paper addresses the visibility-based pursuit-evasion problem where a team of pursuer robots operating in a two-dimensional polygonal space seek to establish visibility of an arbitrarily fast evader. This is a computationally challenging task for which the best known complete algorithm takes time doubly exponential in the number of robots. However, recent advances that utilize sampling-based methods have shown progress in generating feasible solutions. An aspect of this problem that has yet to be explored concerns how to ensure that the robots can recover from catastrophic failures which leave one or more robots unexpectedly incapable of continuing to contribute to the pursuit of the evader. To address this issue, we propose an algorithm that can rapidly recover from catastrophic failures. When such failures occur, a replanning occurs, leveraging both the information retained from the previous iteration and the partial progress of the search completed before the failure to generate a new motion strategy for the reduced team of pursuers. We describe an implementation of this algorithm and provide quantitative results that show that the proposed method is able to recover from robot failures more rapidly than a baseline approach that plans from scratch.

This paper addresses the problem of planning for visibility-based pursuit evasion, in contexts where the pursuer robot may experience some positioning errors as it moves in search of the evader. Specifically, we consider the case in which a pursuer with an omnidirectional sensor searches a known environment to locate an evader that may move arbitrarily quickly. Known algorithms for this problem are based on decompositions of the environment into regions, followed by a search for a sequence of those regions through which the pursuer should pass. In this paper, we note that these regions can be arbitrarily small, and thus that the movement accuracy required of the pursuer may be arbitrarily high. To resolve this limitation, we introduce the notion of an ε-robust solution strategy, in which ε is an upper bound on the positioning error that the pursuer may experience. We establish sufficient conditions under which a solution strategy is ε-robust, and introduce an algorithm that determines, for a given environment, the largest value of ε for which a solution strategy satisfying those sufficient conditions exists. We de-scribe an implementation and show simulated results demonstrating the effectiveness of the approach.

We consider a visibility-based pursuit-evasion problem in which a single robot with an omnidirectional but unreliable sensor moving through an environment must systematically search that environment to detect an unpredictably moving target. A common assumption in visibility-based pursuit-evasion is that the sensors used to detect the evader are perfectly reliable. That is, any evader that moves within view of the pursuer for any interval of time will be detected. This assumption is problematic because, when implemented on real sensor systems, such plans cannot account for the possibility of short-term false negative errors in evader detection. This paper addresses this limitation by introducing a model based on the idea of pessimal unoccluded distance to reason about the degree of plausibility that the evader may be concealed within each occluded region. We describe a decomposition of the environment that fully characterizes the opportune moment for an evader to take advantage of sensor error. Furthermore, we present a complete algorithm that solves the active problem of planning a search for a pursuer which maximizes the distance that the evader must travel through the pursuer robot's sensor footprint.

We introduce a complete algorithm for solving a pursuit-evasion problem in a simply-connected two-dimensional environment, for the case of a single pursuer equipped with fixed beam sensors. The input for our algorithm is an environment and a collection of sensor directions, in which each is capable of line-of-sight detection in a fixed direction. The output is a pursuer motion strategy that ensures the detection of an evader that moves with unbounded speed, or a statement that no such strategy exists. The intuition of the algorithmis to decompose the environment into a collection of convex conservative regions, within which the evader cannot sneak between any pair of adjacent sensors. This decomposition induces a graph we call the pursuit-evasion graph (PEG), such that any correct solution strategy can be expressed as a path through the PEG. For an instance defined by m beams and an environment with n vertices, the algorithm runs in time O(2mn2). We implemented the algorithm in simulation and present some computed examples illustrating the algorithm's correctness.

We present an algorithm that uses a sparse collection of noisy sensors to characterize the observed behavior of a mobile agent. Our approach models the agent's behavior using a collection of randomized simulators called implicit agent models and seeks to classify the agent according to which of these models is believed to be governing its motions. To accomplish this, we introduce an algorithm whose input is an observation sequence generated by the agent, represented as sensor label-time pairs, along with an observation sequence generated by one of our implicit agent models and whose output is a measure of the similarity between the two observation sequences. Using this similarity measure, we propose two algorithms for the model classification problem: one based on a weighted voting scheme and one that uses intermediate resampling steps. We have implemented these algorithms in simulation, and present results demonstrating their effectiveness in correctly classifying mobile agents.

We introduce a centralized algorithm for a visibility-based pursuit-evasion problem in a two-dimensional environment for the case of multiple pursuers. The input for our algorithm is an environment represented as a doubly-connected edge list and the initial positions of the pursuers. The output is a joint strategy for the pursuers that guarantees that the evader has been captured, or a statement that no such strategy exists. We create a Cylindrical Algebraic Decomposition(CAD) of the joint configuration space by using polynomials that capture where critical changes can occur to the region of the environment hidden from the pursuers. Then after computing the adjacency graph for the CAD we construct a Pursuit Evasion Graph(PEG) induced by the adjacency graph. A search through the PEG can produce one of the following outcomes; the search can reach a vertex where the pursuers' motions up to this point ensure that the evader has been captured, or the search terminates without finding a solution and produces a statement recognizing that no solution exists.

We introduce a probabilistically complete algorithm for solving a visibility-based pursuit-evasion problem in two-dimensional polygonal environments with multiple pursuers. The inputs for our algorithm are an environment and the initial positions of the pursuers. The output is a joint strategy for the pursuers that guarantees that the evader has been captured. We create a Sample-Generated Pursuit-Evasion Graph (SG-PEG) that utilizes an abstract sample generator to search the pursuers' joint configuration space for a pursuer solution strategy that captures the evaders. We implemented our algorithm in simulation and provide results.

We present an algorithm that computes a minimal-cost pursuer trajectory for a single pursuer to solve the visibility-based pursuit-evasion problem in a simply-connected two-dimensional environment. This algorithm improves upon the known algorithm of Guibas, Latombe, LaValle, Lin, and Motwani, which is complete but not optimal. Our algorithm uses a Tour of Segments (ToS) subroutine to construct a pursuer path that minimizes the distance traveled by the pursuer while guaranteeing that all evaders in the environment will be captured. We have implemented our algorithm in simulation and provide results.

We propose an algorithm for a visibility-based pursuit-evasion problem in a simply-connected two-dimensional environment, in which a single pursuer has access to a probabilistic model describing how the evaders are likely to move in the environment. The application of our algorithm can be best viewed in the context of search and rescue: Although the victims (evaders) are not actively trying to escape from the robot, it is necessary to consider the task of locating the victims as a pursuit-evasion problem to obtain a firm guarantee that all of the victims are found. We present an algorithm that draws sample evader trajectories from the probabilistic model to compute a plan that lowers the Expected Time to Capture the evaders without drastically increasing the Guaranteed Time to Capture the evaders. We introduce a graph structure that takes advantage of the sampled evader trajectories to compute a path that would "see" all the evaders if they followed only those trajectories in our sampled set. We then use a previous technique to append our path with actions that provide a complete solution for the visibility-based pursuit evasion problem. The resulting plan guarantees that all evaders are located, even if they do not obey the given probabilistic motion model. We implemented the algorithm in a simulation and provide a quantitative comparison to existing methods.