We extend the notion of k-automatic sequences to Ostrowski-automatic sequences, and develop a procedure to computationally decide certain combinatorial and enumeration questions about such sequences that can be expressed as predicates in first-order logic. Our primary contribution is the design and implementation of an adder recognizing addition in a generalized Ostrowski numeration system. We also provide applications of our work to several topics in combinatorics on words, including repetitions and pattern avoidance. We partially resolve a previous conjecture about balanced words by Rampersad et al., and make the first progress on an open problem on rich words by Vesti. We also prove some known results about Lucas words using only machine computation.

我们将k自动序列的概念扩展到Ostrowski自动序列，并开发一种程序来计算确定有关此类序列的某些组合和枚举问题，这些问题可以表示为一阶逻辑中的谓词。我们的主要贡献是设计和实现加法器，该加法器识别广义Ostrowski计数系统中的加法。我们还将我们的工作应用于单词组合词的多个主题，包括重复和模式避免。我们部分地解决了Rampersad等人关于平衡词的先前猜想，并在Vesti关于富词的开放问题上取得了第一个进展。我们还仅使用机器计算就证明了有关Lucas单词的一些已知结果。