Search Results (11)

We introduce cumulative tic-tac-toe, a novel variant of the classic $3\times 3$ tic-tac-toe game in which play continues until the board is completely filled. Each player’s final score is determined by the total number of three-in-a-row sequences they form. Using combinatorial game theory (CGT), we establish that under optimal play, the game is a draw, and we characterize its theoretical properties. To empirically validate and optimize practical play, we develop a reinforcement learning (RL) framework based on temporal-difference (TD) learning, which is enhanced with a domain-informed evaluation function to accelerate convergence. The experimental results show that our triplet-coverage difference (TCD) evaluation function reduces the average number of training episodes by approximately 23.1% compared with a random-initialization baseline, a statistically significant improvement at the 5% significance level. These results demonstrate the efficiency of our CGT–RL approach for cumulative tic-tac-toe and suggest that similar methods may be useful for analyzing related combinatorial games. We also discuss potential analogies in domains such as competitive resource allocation and coalition formation, illustrating how cumulative-scoring games connect abstract game-theoretic ideas to practical sequential decision problems. Full article

This paper presents the design and implementation of an integrated robotic system capable of detecting objects through computer vision and making decisions based on logic strategies to perform physical tasks. For that, the system uses a robotic arm to play the Tic-Tac-Toe game utilizing a Q-learning algorithm to determine optimal moves. The system can be controlled using a graphical interface that enables real-time monitoring, facilitating seamless interaction between the user and the robotic arm. Three algorithms with different decision strategies were developed: a random decision algorithm, the MiniMax algorithm, and Q-learning, a reinforcement-learning algorithm. The results obtained highlight the control of the robotic arm using kinematic equations, the training of a robust YOLOv5 model, and the effective learning capability of a Q-learning algorithm. The proposed system presents practical implementation of the robotic system which can be used as a basis for further projects and for teaching robotics. Full article

This paper presents the design and implementation of an XY plotter system for playing Tic-Tac-Toe against a human opponent. The mechatronic system utilizes stepper motors controlled via a microcontroller and a CNC module, enabling precise bidirectional movement. A vision-based algorithm detects user moves and processes game logic through a Minimax strategy for optimal decision-making. The study highlights the integration of robotics and human–computer interaction, demonstrating potential applications in automation, education, and interactive entertainment. Experimental results validate the system’s accuracy and efficiency in real-time gameplay scenarios. Additionally, the work emphasizes the reliability and predictability of a mathematics-based approach—embodied by the deterministic Minimax algorithm—over AI-driven methods, which may involve uncertainties or probabilistic failure. This highlights the advantage of using well-defined algorithmic logic for tasks requiring consistent performance and outcome guarantees. Full article

This study investigates the strategic decision-making abilities of large language models (LLMs) via the game of Tic-Tac-Toe, renowned for its straightforward rules and definitive outcomes. We developed a mobile application coupled with web services, facilitating gameplay among leading LLMs, including Jurassic-2 Ultra by AI21, Claude 2.1 by Anthropic, Gemini-Pro by Google, GPT-3.5-Turbo and GPT-4 by OpenAI, Llama2-70B by Meta, and Mistral Large by Mistral, to assess their rule comprehension and strategic thinking. Using a consistent prompt structure in 10 sessions for each LLM pair, we systematically collected data on wins, draws, and invalid moves across 980 games, employing two distinct prompt types to vary the presentation of the game’s status. Our findings reveal significant performance variations among the LLMs. Notably, GPT-4, GPT-3.5-Turbo, and Llama2 secured the most wins with the list prompt, while GPT-4, Gemini-Pro, and Mistral Large excelled using the illustration prompt. GPT-4 emerged as the top performer, achieving victory with the minimum number of moves and the fewest errors for both prompt types. This research introduces a novel methodology for assessing LLM capabilities using a game that can illuminate their strategic thinking abilities. Beyond enhancing our comprehension of LLM performance, this study lays the groundwork for future exploration into their utility in complex decision-making scenarios, offering directions for further inquiry and the exploration of LLM limits within game-based frameworks. Full article

Metaheuristic optimization algorithms play a crucial role in optimization problems. However, the traditional identification methods have the following problems: (1) difficulties in nonlinear data processing; (2) high error rates caused by local stagnation; and (3) low classification rates resulting from premature convergence. This paper proposed a variant based on the gray wolf optimization algorithm (GWO) with chaotic disturbance, candidate migration, and attacking mechanisms, naming it the enhanced gray wolf optimizer (EGWO), to solve the problem of premature convergence and local stagnation. The performance of the EGWO was tested on IEEE CEC 2014 benchmark functions, and the results of the EGWO were compared with the performance of three GWO variants, five traditional and popular algorithms, and six recent algorithms. In addition, EGWO optimized the weights and biases of a multi-layer perceptron (MLP) and proposed an EGWO-MLP disease identification model; the model was tested on IEEE CEC 2014 benchmark functions, and EGWO-MLP was verified by UCI dataset including Tic-Tac-Toe, Heart, XOR, and Balloon datasets. The experimental results demonstrate that the proposed EGWO-MLP model can effectively avoid local optimization problems and premature convergence and provide a quasi-optimal solution for the optimization problem. Full article

In this paper, we studied the effects of using Microsoft HoloLens 2 in a Metaverse-based collaborative mixed reality environment on the driver’s social presence while using an autonomous driving system. In (semi-) autonomous vehicles the driver is the system’s monitor, and the driving process becomes a secondary task. Our approach is motivated by the advent of Microsoft Mesh XR technology that enables immersion in multi-person, shared mixed reality environments. We conducted a user study comparing the effects on social presence in two scenarios: baseline and mixed reality collaboration. During the baseline condition, participants communicated and interacted with another person using Skype/Meet which was installed on a mobile tablet. In the second scenario the participants used the Microsoft Mesh application installed on HoloLens 2 to collaborate in a mixed reality environment where each user is represented by an augmented 3D avatar. During the experiment, the participant had to perform a social interaction tell-a-lie task and a remote collaborative tic-tac-toe game, while also monitoring the vehicle’s behavior. The social presence was measured using the Harms and Biocca questionnaire, one of the most widely used tools for evaluating the user’s experience. We found that there are significant statistical differences for Co-presence, Perceived Emotional Interdependence, and Perceived Behavioral Interdependence, and participants were able to easily interact with the avatar in the mixed reality scenario. The proposed study procedure could be taken further to assess the driver’s performance during handover procedures, especially when the autonomous driving system encounters a critical situation. Full article

Temporal difference (TD) learning is a well-known approach for training automated players in board games with a limited number of potential states through autonomous play. Because of its directness, TD learning has become widespread, but certain critical difficulties must be solved in order for it to be effective. It is impractical to train an artificial intelligence (AI) agent against a random player since it takes millions of games for the agent to learn to play intelligently. Training the agent against a methodical player, on the other hand, is not an option owing to a lack of exploration. This article describes and examines a variety of hybrid training procedures for a TD-based automated player that combines randomness with specified plays in a predetermined ratio. We provide simulation results for the famous tic-tac-toe and Connect-4 board games, in which one of the studied training strategies significantly surpasses the other options. On average, it takes fewer than 100,000 games of training for an agent taught using this approach to act as a flawless player in tic-tac-toe. Full article

Automatically generating executable code has a long history of arguably modest success, mostly limited to the generation of small programs of up to 200 lines of code, and genetic improvement of existing code. We present the use of genetic programming (GP) in conjunction with context-oriented behavioral programming (COBP), the latter being a programming paradigm with unique characteristics that facilitate automatic coding. COBP models a program as a set of behavioral threads (b-threads), each aligned to a single behavior or requirement of the system. To evolve behavioral programs we design viable and effective genetic operators, a genetic representation, and evaluation methods. The simplicity of the COBP paradigm, its straightforward syntax, the ability to use verification and formal-method techniques to validate program correctness, and a program comprising small independent chunks all allow us to effectively generate behavioral programs using GP. To demonstrate our approach we evolve complete programs from scratch of a highly competent O player for the game of tic-tac-toe. The evolved programs are well structured, consisting of multiple, explainable modules that specify the different behavioral aspects of the program and are similar to our handcrafted program. To validate the correctness of our individuals, we utilize the mathematical characteristics of COBP to analyze program behavior under all possible execution paths. Our analysis of an evolved program proved that it plays as expected more than 99% of the times. Full article

The study of twisted bilayer 2D materials has revealed many interesting physics properties. A twisted moiré photonic crystal is an optical analog of twisted bilayer 2D materials. The optical properties in twisted photonic crystals have not yet been fully elucidated. In this paper, we generate 2D twisted moiré photonic crystals without physical rotation and simulate their photonic band gaps in photonic crystals formed at different twisted angles, different gradient levels, and different dielectric filling factors. At certain gradient levels, interface modes appear within the photonic band gap. The simulation reveals “tic tac toe”-like and “traffic circle”-like modes as well as ring resonance modes. These interesting discoveries in 2D twisted moiré photonic crystal may lead toward its application in integrated photonics. Full article

Background: Sports vision is a specialisation of optometry whose objective is to improve and preserve visual function to increase sports performance. The main objective of the present study was to compare the visual expertise of non-athletes to skeet shooting athletes. Methods: Participants underwent an optometric assessment in which all those with severe deviations from normal vision, after compensating for visual abnormalities, were eliminated. After that, the following six visuospatial components were measured: hand–eye coordination, peripheral awareness, fixation disparity, saccadic eye movements, speed of recognition and visual memory. To measure the aforementioned components, the following tests were used: directional arrows, similar and different characters, the dichromatic disparity test, character marking, a tachistoscopic test and tic-tac-toe using COI-vision software. Results: Skeet shooting athletes performed significatively better (p ≤ 0.05) in two out of the six tests: hand–eye coordination and visual memory. Conclusions: Although this study does not support the theory that athletes—in this case, skeet shooting athletes—perform significantly better in most components of the visuospatial tests, visual memory and hand–eye coordination are exceptions. To be more accurate in distinguishing between athletes and non-athletes, specific testing methods that can be used by a wide variety of disciplines should be developed. Training the weakest aspects of athletes can improve their sports performance. Full article

The ease of interpretation of a classification model is essential for the task of validating it. Sometimes it is required to clearly explain the classification process of a model’s predictions. Models which are inherently easier to interpret can be effortlessly related to the context of the problem, and their predictions can be, if necessary, ethically and legally evaluated. In this paper, we propose a novel method to generate rule-based classifiers from categorical data that can be readily interpreted. Classifiers are generated using a multi-objective optimization approach focusing on two main objectives: maximizing the performance of the learned classifier and minimizing its number of rules. The multi-objective evolutionary algorithms ENORA and NSGA-II have been adapted to optimize the performance of the classifier based on three different machine learning metrics: accuracy, area under the ROC curve, and root mean square error. We have extensively compared the generated classifiers using our proposed method with classifiers generated using classical methods such as PART, JRip, OneR and ZeroR. The experiments have been conducted in full training mode, in 10-fold cross-validation mode, and in train/test splitting mode. To make results reproducible, we have used the well-known and publicly available datasets Breast Cancer, Monk’s Problem 2, Tic-Tac-Toe-Endgame, Car, kr-vs-kp and Nursery. After performing an exhaustive statistical test on our results, we conclude that the proposed method is able to generate highly accurate and easy to interpret classification models. Full article