Large language models (LLMs) have exhibited impressive performance in language comprehension and various reasoning tasks. However, their abilities in spatial reasoning, a crucial aspect of human cognition, remain relatively unexplored. Human possess a remarkable ability to create mental images of unseen objects and actions through a process known as the Mind's Eye, enabling the imagination of the unseen world. Inspired by this cognitive capacity, we propose Visualization-of-Thought (VoT) prompting. VoT aims to elicit spatial reasoning of LLMs by visualizing their reasoning traces, thereby guiding subsequent reasoning steps. We employed VoT for multi-hop spatial reasoning tasks, including natural language navigation, visual navigation, and visual tiling in 2D grid worlds. Experimental results demonstrated that VoT significantly enhances the spatial reasoning abilities of LLMs. Notably, VoT outperformed existing multimodal large language models (MLLMs) in these tasks. While VoT works surprisingly well on LLMs, the ability to generate mental images to facilitate spatial reasoning resembles the mind's eye process, suggesting its potential viability in MLLMs.

The game of Othello is one of the world's most complex and popular games that has yet to be computationally solved. Othello has roughly ten octodecillion (10 to the 58th power) possible game records and ten octillion (10 to the 28th power) possible game positions. The challenge of solving Othello, determining the outcome of a game with no mistake made by either player, has long been a grand challenge in computer science. This paper announces a significant milestone: Othello is now solved. It is computationally proved that perfect play by both players lead to a draw. Strong Othello software has long been built using heuristically designed search techniques. Solving a game provides a solution that enables the software to play the game perfectly.

Gomoku, also known as five in a row, is a classical board game, ideally suited for quickly testing novel Artificial Intelligence (AI) techniques. With the aim of facilitating a developer willing to write a new Gomoku player, in this report we present an analysis of the main game concepts and strategies, which is wider and deeper than existing ones. Moreover, after discussing the general structure of an artificial player, we present and analyse a strong Gomoku player, named Wine, the code of which is freely available on the Internet and which is an excelent example of how a modern player is organised.

This paper presents aplib, a Java library for programming intelligent agents, featuring BDI and multi agency, but adding on top of it a novel layer of tactical programming inspired by the domain of theorem proving. Aplib is also implemented in such a way to provide the fluency of a Domain Specific Language (DSL). Compared to dedicated BDI agent programming languages such as JASON, 2APL, or GOAL,aplib's embedded DSL approach does mean that \aplib\ programmers will still be limited by Java syntax, but on other hand they get all the advantages that Java programmers get: rich language features (object orientation, static type checking, $\lambda$-expression, libraries, etc), a whole array of development tools, integration with other technologies, large community, etc.

This article is my entry for CodeProject's AI competition "Image Classification Challenge"[ ]. My goal was to teach a neural network to play a game of tic tac toe, starting from only knowing the rules. Tic tac toe is a solved game. A perfect strategy[ ] exists so a neural network is a bit overkill and will not perform as well as existing programs and humans can. Described from a high level: when the AI needs to make a move, it iterates over all possible moves, generates the board after making a given move, and uses the neural network to see how good the position is after performing that move.

Temperature Discovery Search (TDS) is a forward search method for computing or approximating the temperature of a combinatorial game. Temperature and mean are important concepts in combinatorial game theory, which can be used to develop efficient algorithms for playing well in a sum of subgames. A new algorithm TDS+ with five enhancements of TDS is developed, which greatly speeds up both exact and approximate versions of TDS. Means and temperatures can be computed faster, and fixed-time approximations which are important for practical play can be computed with higher accuracy than before.