Decidability for Sturmian words
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Published:2024-08-05
Issue:
Volume:Volume 20, Issue 3
Page:
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ISSN:1860-5974
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Container-title:Logical Methods in Computer Science
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language:en
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Author:
Hieronymi Philipp,Ma Dun,Oei Reed,Schaeffer Luke,Schulz Christian,Shallit Jeffrey
Abstract
We show that the first-order theory of Sturmian words over Presburger
arithmetic is decidable. Using a general adder recognizing addition in
Ostrowski numeration systems by Baranwal, Schaeffer and Shallit, we prove that
the first-order expansions of Presburger arithmetic by a single Sturmian word
are uniformly $\omega$-automatic, and then deduce the decidability of the
theory of the class of such structures. Using an implementation of this
decision algorithm called Pecan, we automatically reprove classical theorems
about Sturmian words in seconds, and are able to obtain new results about
antisquares and antipalindromes in characteristic Sturmian words.
Publisher
Centre pour la Communication Scientifique Directe (CCSD)