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MIDTERM Is a Deterministic Technique to Exit Recursive Mazes

Authors Charles Bouillaguet , Orel Cosseron

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Subject Classification

ACM Subject Classification
  • Theory of computation → Grammars and context-free languages
  • Theory of computation → Graph algorithms analysis
Keywords
  • Recursive maze
  • pushdown automaton
  • reachability
  • context-free grammar
  • graph rewriting

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Abstract

A recursive maze is a maze that contains copies of itself (that themselves contain copies of themselves, etc.). To exit the maze or reach the goal, each recursive block that has been entered must be exited. These once-popular puzzles are difficult to solve by hand, and this begs for an algorithmic solution.
It has been observed many times in the past that a recursive maze can be represented by a deterministic pushdown automaton. Finding a path, possibly the shortest, that leads to an exit therefore reduces to finding a word in a context-free language described by such an automaton. The problem is well-known to be decidable, and there is a classical algorithm for this task. We present a new algorithm, Midterm, with improved complexity compared to existing solutions.
Midterm improves on a previous attempt called Longterm (Obviously Not a Good Technique to Exit Recursive Mazes).

Cite As Get BibTex

Charles Bouillaguet and Orel Cosseron. MIDTERM Is a Deterministic Technique to Exit Recursive Mazes. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.9

Author Details

Charles Bouillaguet
  • LIP6 laboratory, Sorbonne Université, Paris, France
Orel Cosseron
  • Independent researcher, Paris, France

Acknowledgements

We thank Ambroise Fleury for involuntarily suggesting this work, and the anonymous reviewers for their constructive feedback as well as for spotting many, many typos.

References

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