Compass-free Navigation of Mazes

13 pages•Published: March 27, 2016

Abstract

If you find yourself in a corridor of a standard maze, a sure and easy way to escape
is to simply pick the left (or right) wall, and then follow it along its twists and
turns and around the dead-ends till you eventually arrive at the exit. But what
happens when you cannot tell left from right? What if you cannot tell North from
South? What if you cannot judge distances, and have no idea what it means to follow
a wall in a given direction?

The possibility of escape in these circumstances is suggested in the statement of an
unproven theorem given in David Hilbert's celebrated /Foundations of Geometry/, in
which he effectively claimed that a standard maze could be fully navigated using
axioms and concepts based /solely/ on the relations of points lying on lines in a
specified order.

We discuss our algorithm for this surprisingly challenging version of the maze
navigation problem, and our HOL Light verification of its correctness from Hilbert's
axioms.

Keyphrases: formalized mathematics, geometry, interactive theorem proving

In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 143--155

Links:	https://easychair.org/publications/paper/bnqW
	https://doi.org/10.29007/9djp