Hyperbolic Minesweeper Is in P

We show that, while Minesweeper is NP-complete, its hyperbolic variant is in P. Our proof does not rely on the rules of Minesweeper, but is valid for any puzzle based on satisfying local constraints on a graph embedded in the hyperbolic plane

A Constraint-Based Approach to Solving Minesweeper

·Motivate the students for the study of Constraint Processing (CP). Minesweeper is perfect to this end because it allows us to illustrate the use of CP algorithms in a familiar context and show how they operate. ·Understand and demystify humans’ fascination with puzzles. ·Discourage graduate students from losing too much time playing the game by making a program that plays the game for them

A Phase Transition in Minesweeper

We study the average-case complexity of the classic Minesweeper game in which players deduce the locations of mines on a two-dimensional lattice. Playing Minesweeper is known to be co-NP-complete. We show empirically that Minesweeper exhibits a phase transition analogous to the well-studied SAT phase transition. Above the critical mine density it becomes almost impossible to play Minesweeper by logical inference. We use a reduction to Boolean unsatisfiability to characterize the hardness of Minesweeper instances, and show that the hardness peaks at the phase transition. Furthermore, we demonstrate algorithmic barriers at the phase transition for polynomial-time approaches to Minesweeper inference. Finally, we comment on expectations for the asymptotic behavior of the phase transition

Develop heuristics to the popular Minesweeper game

This project describes Automine, a program intended to aid in the solving of the Minesweeper computer game. Automine is based on the Linux xwindow C program with xwindow graphic library. The program uses heuristics and probability statistics to help in determining safe squares and squares concealing mines with the goal of allowing a player to achieve minimal time performance. The source code for Automine and for a game simulation is provided in the appendices

LIGHTYEAR: Using Modularity to Scale BGP Control Plane Verification

Current network control plane verification tools cannot scale to large networks, because of the complexity of jointly reasoning about the behaviors of all nodes in the network. In this paper we present a modular approach to control plane verification, whereby end-to-end network properties are verified via a set of purely local checks on individual nodes and edges. The approach targets the verification of safety properties for BGP configurations and provides guarantees in the face of both arbitrary external route announcements from neighbors and arbitrary node/link failures. We have proven the approach correct and also implemented it in a tool called Lightyear. Experimental results show that Lightyear scales dramatically better than prior control plane verifiers. Further, we have used Lightyear to verify three properties of the wide area network of a major cloud provider, containing hundreds of routers and tens of thousands of edges. To our knowledge no prior tool has been demonstrated to provide such guarantees at that scale. Finally, in addition to the scaling benefits, our modular approach to verification makes it easy to localize the causes of configuration errors and to support incremental re-verification as configurations are updatedComment: 12 pages (+ 2 pages references), 3 figures submitted to NSDI '2

Assessing Logical Puzzle Solving in Large Language Models: Insights from a Minesweeper Case Study

Large Language Models (LLMs) have shown remarkable proficiency in language understanding and have been successfully applied to a variety of real-world tasks through task-specific fine-tuning or prompt engineering. Despite these advancements, it remains an open question whether LLMs are fundamentally capable of reasoning and planning, or if they primarily rely on recalling and synthesizing information from their training data. In our research, we introduce a novel task -- Minesweeper -- specifically designed in a format unfamiliar to LLMs and absent from their training datasets. This task challenges LLMs to identify the locations of mines based on numerical clues provided by adjacent opened cells. Successfully completing this task requires an understanding of each cell's state, discerning spatial relationships between the clues and mines, and strategizing actions based on logical deductions drawn from the arrangement of the cells. Our experiments, including trials with the advanced GPT-4 model, indicate that while LLMs possess the foundational abilities required for this task, they struggle to integrate these into a coherent, multi-step logical reasoning process needed to solve Minesweeper. These findings highlight the need for further research to understand and nature of reasoning capabilities in LLMs under similar circumstances, and to explore pathways towards more sophisticated AI reasoning and planning models.Comment: 24 pages, 5 figures, 3 table