Inclusion Diagrams for Classes of Deterministic Bottom-up Tree-to-Tree-Series Transformations

• Main Author: Maletti, Andreas
• Other Authors: Technische Universität Dresden, Fakultät Informatik
• Format: Others
• Language: English
• Published: Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden 2012
• Subjects: bottom-up tree-to-tree-series; tree series; tree series transducers; ddc:004; rvk:SS 5514
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-99211; http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-99211; http://www.qucosa.de/fileadmin/data/qucosa/documents/9921/tud_TB_2004-07.pdf

In this paper we investigate the relationship between classes of tree-to-tree-series (for short: t-ts) and o-tree-to-tree-series (for short: o-t-ts) transformations computed by restricted deterministic bottom-up weighted tree transducers (for short: deterministic bu-w-tt). Essentially, deterministic bu-w-tt are deterministic bottom-up tree series transducers [EFV02, FV03, ful, FGV04], but the former are de ned over monoids whereas the latter are de ned over semirings and only use the multiplicative monoid thereof. In particular, the common restrictions of non-deletion, linearity, totality, and homomorphism [Eng75] can equivalently be de ned for deterministic bu-w-tt. Using well-known results of classical tree transducer theory (cf., e.g., [Eng75, Fül91]) and also new results on deterministic bu-w-tt, we order classes of t-ts and o-t-ts transformations computed by restricted deterministic bu-w-tt by set inclusion. More precisely, for every commutative monoid we completely specify the inclusion relation of the classes of t-ts and o-t-ts transformations for all sensible combinations of restrictions by means of inclusion diagrams.