Classes of tree homomorphisms with decidable preservation of regularity

Authors:
Guillem Godoy;Sebastian Maneth;Sophie Tison
Affiliations:
Universitat Politècnica de Catalunya, Barcelona, Spain;NICTA and UNSW, Sydney, Australia;Université des Sciences et Technologies de Lille, Villeneuve d'Ascq Cedex, France
Venue:
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Year:
2008

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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.