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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.
CitationCreus, C. [et al.]. The HOM problem is EXPTIME-complete. A: IEEE Logic in Computer Science. "Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012". 2012, p. 255-264.
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