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从模式到迷宫结构:基于SMT的路径合成与二维/三维构建

From Patterns to Maze Structures: SMT-Based Path Synthesis and 2D/3D Construction

Shengyi Wang

arXiv 2607.09781首次发表:更新:

发表机构

Shanghai Qi Zhi Institute(上海期智研究院)

机构由 AI 辅助整理,请以论文原文为准。

AI 中文总结

该研究提出从输入模式构建迷宫结构的流程,将核心路径合成问题编码为可满足性模理论中的全局约束求解,所得路径为构建平面和三维迷宫提供框架,还通过更多示例及阐述扩展了会议论文。

AI 中文摘要

我们提出了一个从文本或形状等输入模式构建迷宫结构的流程。核心路径合成问题被编码为可满足性模理论中的邻接、连续性和模式约束覆盖的全局约束,每个固定边界实例可通过一次调用求解。得到的路径可以是平面自回避路线或具有规定上下交叉的分层遍历,为构建平面迷宫和编织迷宫的三维实现提供框架。本报告通过更具代表性的SMT-LIB示例以及对合成路径如何成为平面和三维形式的具体迷宫构建的更全面阐述,扩展了已发表的Bridges 2026会议论文。

英文摘要

We present a pipeline for constructing maze structures from input patterns such as text or shapes. The central path-synthesis problem is encoded in Satisfiability Modulo Theories as global constraints on adjacency, continuity, and pattern-constrained coverage, allowing each fixed-bound instance to be solved in one call. The resulting path is either a planar, self-avoiding route or a layered traversal with prescribed over--under crossings, and it serves as a scaffold for constructing planar mazes and three-dimensional realizations of woven mazes. This report extends the published Bridges 2026 conference paper with more representative SMT-LIB examples and a fuller account of how synthesized paths become concrete maze constructions in planar and three-dimensional form.

Comments14 pages, 7 figures

论文原文

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