NDLI: The HOM problem is decidable

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The HOM problem is decidable

Content Provider	ACM Digital Library
Author	Àlvarez, Carme Giménez, Omer Godoy, Guillem Ramos, Lander
Abstract	We provide an algorithm that, given a tree homomorphism H and a regular tree language L represented by a tree automaton, determines whether H(L) is regular. This settles a question that has been open for a long time. Along the way, we develop new constructions and techniques which are interesting by themselves, and provide several significant intermediate results. For example, we prove that the universality problem is decidable for languages represented by tree automata with equality constraints, and that the equivalence and inclusion problems are decidable for images of regular tree languages through tree homomorphisms. Our algorithms are based on the following constructions. We describe a simple transformation for converting a tree automaton with equality constraints into a tree automaton with inequality constraints recognizing the complementary language. We also define a new class of automata with arbitrary inequality constraints and a particular kind of equality constraints. An automaton of this new class essentially recognizes the intersection of a tree automaton with inequality constraints and the image of a regular tree language through a tree homomorphism. We prove decidability of emptiness and finiteness for this class by a pumping mechanism.
Starting Page	485
Ending Page	494
Page Count	10
File Format	PDF
ISBN	9781450300506
DOI	10.1145/1806689.1806757
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-06-05
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Homomorphisms Regular languages Transducers Tree automata
Content Type	Text
Resource Type	Article

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