dc.contributor.author Godoy, Guillem dc.contributor.author Giménez, Omer dc.contributor.author Ramos Garrido, Lander dc.contributor.author Álvarez Faura, M. del Carme dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.contributor.other Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics dc.date.accessioned 2016-06-14T11:51:17Z dc.date.available 2016-06-14T11:51:17Z dc.date.issued 2009-06 dc.identifier.citation Godoy, G., Giménez, O., Ramos, L., Álvarez, C. "The HOM problem is decidable". 2009. dc.identifier.uri http://hdl.handle.net/2117/87972 dc.description.abstract We close affirmatively a question which has been open for 35 years: decidability of the HOM problem. The HOM problem consists in deciding, given a tree homomorphism $H$ and a regular tree languagle $L$ represented by a tree automaton, whether $H(L)$ is regular. For deciding the HOM problem, 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 languages through tree homomorphisms. Our contributions are based on the following new results. We describe a simple transformation for converting a tree automaton with equality constraints into a tree automaton with disequality constraints recognizing the complementary language. We also define a new class of automaton with arbitrary disequality constraints and a particular kind of equality constraints. This new class essentially recognizes the intersection of a tree automaton with disequality constraints and the image of a regular language through a tree homomorphism. We prove decidability of emptiness and finiteness for this class by a pumping mechanism. The above constructions are combined adequately to provide an algorithm deciding the HOM problem. dc.format.extent 39 p. dc.language.iso eng dc.relation.ispartofseries LSI-09-22-R dc.subject Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica dc.subject.other Tree automata dc.subject.other Tree homomorphisms dc.subject.other Hom problem dc.title The HOM problem is decidable dc.type External research report dc.contributor.group Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals dc.rights.access Open Access local.identifier.drac 18558837 dc.description.version Postprint (published version) local.citation.author Godoy, G.; Giménez, O.; Ramos, L.; Álvarez, C.
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