Decidability of regularity preservation by a homomorphism is a well known open problem for regular tree languages. Two interesting subclasses of this problem are considered: first, it is proved that regularity preservation is decidable in polynomial time when the domain language is constructed over a monadic signature, i.e., over a signature where all symbols have arity 0 or 1. Second, decidability is proved for the case where non-linearity of the homomorphism is restricted to the root node (or nodes of bounded depth) of any input term. The latter result is obtained by proving decidability of this problem: Given a set of terms with regular constraints on the variables, is its set of ground instances regular? This extends previous results where regular constraints where not considered. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Godoy, G., Maneth, S., & Tison, S. (2008). Classes of tree homomorphisms with decidable preservation of regularity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4962 LNCS, pp. 127–141). https://doi.org/10.1007/978-3-540-78499-9_10
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