Properties of Quasi-Relabeling Tree Bimorphisms

The fundamental properties of the class QUASI of quasi-relabeling relations are investigated. A quasi-relabeling relation is a tree relation that is dened by a tree bimorphism (ϕ, L, ψ), where ϕ and ψ are quasi-relabeling tree homomorphisms and L is a regular tree language. Such relations admit a canonical representation, which immediately also yields that QUASI is closed under nite union. However, QUASI is not closed under intersection and complement. In addition, many standard relations on trees (e.g., branches, subtrees, v-product, v-quotient, and f-top-catenation) are not quasi-relabeling relations. If quasi-relabeling relations are considered as string relations (by taking the yields of the trees), then every Cartesian product of two context-free string languages is a quasi-relabeling relation. Finally, the connections between quasi-relabeling relations, alphabetic relations, and classes of tree relations dened by several types of top-down tree transducers are presented. T...

• Type: Journal
• Year: 2010
• Where: IJFCS
• Authors: Andreas Maletti, Catalin Ionut Tîrnauca
• Keywords: IJFCS 2010, Quasi-relabeling Relations, Tree, Tree Languages