Abstract
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.
The first author was supported by Spanish Min. of Educ. and Science by the LogicTools project (TIN2004-03382), and by the FORMALISM project (TIN2007-66523).
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Godoy, G., Maneth, S., Tison, S. (2008). Classes of Tree Homomorphisms with Decidable Preservation of Regularity. In: Amadio, R. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2008. Lecture Notes in Computer Science, vol 4962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78499-9_10
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