The HOM Problem is EXPTIME-Complete

Authors:
Carles Creus;Adrià Gascon;Guillem Godoy;Lander Ramos
Affiliations:
-;-;-;-
Venue:
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Year:
2012

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Abstract

The HOM problem questions whether the image of a given regular tree language through a given tree homomorphism is also regular. Decidability of HOM is an important theoretical question which was open for a long time. Recently, HOM has been proved decidable with a triple exponential time algorithm. In this paper we obtain an exponential time algorithm for this problem, and conclude that it is EXPTIME-complete. The proof builds upon previous results and techniques on tree automata with constraints.