تقرير
Decidability for Sturmian words
| العنوان: | Decidability for Sturmian words |
|---|---|
| المؤلفون: | Hieronymi, Philipp, Ma, Dun, Oei, Reed, Schaeffer, Luke, Schulz, Christian, Shallit, Jeffrey |
| المصدر: | Logical Methods in Computer Science, Volume 20, Issue 3 (August 5, 2024) lmcs:9980 |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Logic in Computer Science, Mathematics - Combinatorics, Mathematics - Logic |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.46298/lmcs-20(3:12)2024 |
| URL الوصول: | http://arxiv.org/abs/2102.08207 |
| رقم الأكسشن: | edsarx.2102.08207 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.46298/lmcs-20(3:12)2024 |
|---|