Codes and equations on trees

Sabrina Mantaci, Antonio Restivo
2001 Theoretical Computer Science  
The objective of this paper is to study, by new formal methods, the notion of tree code introduced by Nivat in (Tree Automata and Languages, Elsevier, Amsterdam, 1992, pp. 1-19). In particular, we consider the notion of stability for sets of trees closed under concatenation. This allows us to give a characterization of tree codes which is very close to the algebraic characterization of word codes in terms of free monoids. We further deÿne the stable hull of a set of trees and derive a defect
more » ... orem for trees, which generalizes the analogous result for words. As a consequence, we obtain some properties of tree codes having two elements. Moreover, we propose a new algorithm to test whether a ÿnite set of trees is a tree code. The running time of the algorithm is polynomial in the size of the input. We also introduce the notion of tree equation as complementary view to tree codes. The main problem emerging in this approach is to decide the satisÿability of tree equations: it is a special case of second-order uniÿcation, and it remains still open.
doi:10.1016/s0304-3975(99)00317-5 fatcat:7og4auczyvbmjlhu35aimkkgbu