A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On the Solution Sets of Three-Variable Word Equations
Tekijät: Saarela, Aleksi
Kustantaja: SPRINGER
Kustannuspaikka: NEW YORK
Julkaisuvuosi: 2024
Journal: Theory of Computing Systems
Tietokannassa oleva lehden nimi: THEORY OF COMPUTING SYSTEMS
Lehden akronyymi: THEOR COMPUT SYST
Vuosikerta: 68
Numero: 6
Aloitussivu: 1556
Lopetussivu: 1571
Sivujen määrä: 16
ISSN: 1432-4350
eISSN: 1433-0490
DOI: https://doi.org/10.1007/s00224-024-10193-9
Verkko-osoite: https://doi.org/10.1007/s00224-024-10193-9
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/457699339
It is known that the set of solutions of any constant-free three-variable word equation can be represented using parametric words, and the number of numerical parameters and the level of nesting in these parametric words is at most logarithmic with respect to the length of the equation. We show that this result can be significantly improved in the case of unbalanced equations, that is, equations where at least one variable has a different number of occurrences on the left-hand side and on the right-hand side. More specifically, it is sufficient to have two numerical parameters and one level of nesting in this case. We also discuss the possibility of proving a similar result for balanced equations in the future.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
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Open Access funding provided by University of Turku (including Turku University Central Hospital).
