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

2026-07-08

AI Summary

This work proposes an end-to-end approach based on Satisfiability Modulo Theories (SMT) for automatically generating maze paths from arbitrary input patterns—such as text or shapes—that satisfy prescribed topological constraints, with support for both two-dimensional and three-dimensional physical realizations. The method formalizes path synthesis as a global constraint satisfaction problem encompassing adjacency, continuity, and pattern coverage, enabling the generation of self-avoiding planar paths or layered paths with specified over-and-under crossings through a single SMT solving step. To the best of our knowledge, this is the first application of SMT-based formal methods to pattern-driven maze generation, unifying path synthesis and 2D/3D geometric construction. The framework successfully translates textual or graphical inputs into fabricable maze structures, validated through a complete pipeline and demonstrated via representative examples.

Abstract

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.

Problem

• maze generation
• path synthesis
• pattern-constrained coverage
• 2D/3D construction
• SMT

Innovation

• SMT-based path synthesis
• maze generation
• self-avoiding path
• 3D woven maze
• constraint-driven design