Abstract
We introduce the notion of equation on trees, generalizing the corresponding notion for words, and we develop the first steps of a theory of tree equations. The main result of the paper states that, if a pair of trees is the solution of a tree equation with two indeterminates, then the two trees are both powers of the same tree. As an application, we show that a tree can be expressed in a unique way as a power of a primitive tree. This extends a basic result of combinatorics on words to trees. Some open problems are finally proposed.
Cite
CITATION STYLE
Mantaci, S., & Restivo, A. (1996). Equations on trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1113, pp. 443–456). Springer Verlag. https://doi.org/10.1007/3-540-61550-4_169
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