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dc.contributor.authorBaranwal, Aseem 20:38:25 (GMT) 20:38:25 (GMT)
dc.description.abstractWe extend the notion of automatic sequences to a broader class, the Ostrowski-automatic sequences. We develop a procedure for computationally deciding certain combinatorial and enumeration questions about such sequences that can be expressed as predicates in first-order logic. In Chapter 1, we begin with topics and ideas that are preliminary to this work, including a small introduction to non-standard positional numeration systems and the relationship between words and automata. In Chapter 2, we define the theoretical foundations for recognizing addition in a generalized Ostrowski numeration system and formalize the general theory that develops our decision procedure. Next, in Chapter 3, we show how to implement these ideas in practice, and provide the implementation as an integration to the automatic theorem-proving software package -- Walnut. Further, we provide some applications of our work in Chapter 4. These applications span several topics in combinatorics on words, including repetitions, pattern-avoidance, critical exponents of special classes of words, properties of Lucas words, and so forth. Finally, we close with open problems on decidability and higher-order numeration systems and discuss future directions for research.en
dc.publisherUniversity of Waterlooen
dc.subjectdecision proceduresen
dc.subjectOstrowski numerationen
dc.subjectcombinatorics on wordsen
dc.subjectautomatic sequencesen
dc.titleDecision Algorithms for Ostrowski-Automatic Sequencesen
dc.typeMaster Thesisen
dc.pendingfalse R. Cheriton School of Computer Scienceen Scienceen of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorShallit, Jeffrey
uws.contributor.affiliation1Faculty of Mathematicsen

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