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,...
| Autores: | , , , |
|---|---|
| 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 |
| 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. |
|---|