The HOM problem is EXPTIME-complete

We define a new class of tree automata with constraints and prove decidability of the emptiness problem for this class in exponential time. As a consequence, we obtain several EXPTIME-completeness results for problems on images of regular tree languages under tree homomorphisms, like set inclusion,...

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Detalles Bibliográficos
Autores: Creus López, Carles, Gascon Caro, Adrian, Godoy Balil, Guillem, Ramos Garrido, Lander
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/102817
Acceso en línea:https://hdl.handle.net/2117/102817
https://dx.doi.org/10.1137/140999104
Access Level:acceso abierto
Palabra clave:Formal languages
Computational complexity
Machine theory
Homomorphisms
Regular languages
Transducers
Tree automata
Llenguatges formals
Complexitat computacional
Màquines, Teoria de
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Descripción
Sumario:We define a new class of tree automata with constraints and prove decidability of the emptiness problem for this class in exponential time. As a consequence, we obtain several EXPTIME-completeness results for problems on images of regular tree languages under tree homomorphisms, like set inclusion, regularity (HOM problem), and finiteness of set difference. Our result also has implications in term rewriting, since the set of reducible terms of a term rewrite system can be described as the image of a tree homomorphism. In particular, we prove that inclusion of sets of normal forms of term rewrite systems can be decided in exponential time. Analogous consequences arise in the context of XML typechecking, since types are defined by tree automata and some type transformations are homomorphic.