Hamoon Mousavi

On the Number of Unbordered Factors

We illustrate a general technique for enumerating factors of k-automatic sequences by proving a conjecture on the number f(n) of unbordered factors of the Thue-Morse sequence. We show that f(n) = 4 and that f(n) = n infinitely often. We also give examples of automatic sequences having exactly 2 unbordered factors of every length.

Decision algorithms for Fibonacci-automatic Words, I: Basic results

We implement a decision procedure for answering questions about a class of infinite words that might be called (for lack of a better name) “Fibonacci-automatic”. This class includes, for example, the famous Fibonacci word f = f 0 f 1 f 2 ··· = 01001010··· , the fixed point of the morphism 0 → 01 and 1 → 0. We then recover many results about the Fibonacci word from the literature (and improve some of them), such as assertions about the occurrences in f of squares, cubes, palindromes, and so forth.

Decision Algorithms for Fibonacci-Automatic Words, III: Enumeration and Abelian Properties

We continue our study of the class of Fibonacci-automatic words. These are infinite words whose nth term is defined in terms of a finite-state function of the Fibonacci representation of n. In this paper, we show how enumeration questions (such as counting the number of squares of length n in the Fibonacci word) can be decided purely mechanically, using a decision procedure. We reprove some known results, in a unified way, using our technique, and we prove some new results. We also examine abelian properties of these words. As a consequence of our results on abelian properties, we get the result that every nontrivial morphic image of the Fibonacci word is Fibonacci-automatic.

A New Approach to the Paperfolding Sequences

In this paper we show how to re-derive known results about the paperfolding sequences, and obtain new ones, using a new approach using a decision method and some machine computation. We also obtain exact expressions for the recurrence and appearance function of the paperfolding sequences, and solve an open problem of Rampersad about factors shared in common between two different paperfolding sequences.

Shortest Repetition-Free Words Accepted by Automata

We consider the following problem: given that a finite automaton

Filtrations of Formal Languages by Arithmetic Progressions

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Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance.

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Mechanical Proofs of Properties of the Tribonacci Word

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Decision algorithms for Fibonacci-automatic words, II

states accepts at least one

Automatic Theorem Proving in Walnut.

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