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FOSSACS'08, Hungary (2008)
Classes of Tree Homomorphisms with Decidable Preservation of Regularity
Guillem Godoy 1, Sebastian Maneth 2, Sophie Tison 3, 4
(2008-04-02)

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.
1:  Department of Computer Science (LSI)
Technical University of Catalonia
2:  National ICT Australia (NICTA)
Australian National University – University of New South Wales – NSW Government – ACT Government
3:  MOSTRARE (INRIA Futurs)
INRIA – CNRS : UMR8022 – Université Lille I - Sciences et technologies – Université Lille III - Sciences humaines et sociales
4:  Laboratoire d'Informatique Fondamentale de Lille (LIFL)
CNRS : UMR8022 – Université Lille I - Sciences et technologies – Université Lille III - Sciences humaines et sociales – INRIA
Computer Science/Computation and Language

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