10 citations · 14 across the 3 of their papers we have counts for
7 papers
Standard words and solutions of the word equation
Jarkko Peltomäki, Aleksi Saarela
We consider solutions of the word equation such that the squares are minimal squares found in optimal squareful infinite words. We…
Separating many words by counting occurrences of factors
Aleksi Saarela
For a given language , we study the languages such that for all distinct words , there exists a word that appears a different number of times as a fact…
An optimal bound on the solution sets of one-variable word equations and its consequences
Dirk Nowotka, Aleksi Saarela
We solve two long-standing open problems on word equations. Firstly, we prove that a one-variable word equation with constants has either at most three or an infinite number of sol…
Degrees of Infinite Words, Polynomials, and Atoms (Extended Version)
Jörg Endrullis, Juhani Karhumäki Jan Willem Klop, Aleksi Saarela
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal…
On maximal chains of systems of word equations
Juhani Karhumäki, Aleksi Saarela
We consider systems of word equations and their solution sets. We discuss some fascinating properties of those, namely the size of a maximal independent set of word equations, and…
Variations of the Morse-Hedlund Theorem for -Abelian Equivalence
Juhani Karhumäki, Aleksi Saarela, Luca. Q. Zamboni
In this paper we investigate local to global phenomena for a new family of complexity functions of infinite words indexed by $k \in \Ni \cup \{+\infty\}$ where $\Ni$ denotes the se…