Alphabetic tree relations

Properties of quasi-alphabetic tree bimorphisms

We study the class of quasi-alphabetic relations, i.e., tree transformations de ned by tree bimorphisms (';L; ) with '; quasi-alphabetic tree homomorphisms and L a regular tree language. We present a canonical representation of these relations; as an immediate consequence, we get the closure under union. Also, we show that they are not closed under intersection and complement, and do not preser...

Syntax-Directed Translations and Quasi-alphabetic Tree Bimorphisms - Revisited

Quasi-alphabetic tree bimorphisms [Steinby and Tîrn uc : Syntax-Directed Translations and Quasi-Alphabetic Tree Bimorphisms. Proc. CIAA, LNCS 4783:265 276, 2007] are reconsidered. It is known that the class of (string) translations de ned by such bimorphisms coincides with the class of syntax-directed translations. This result is extended to a smaller class of tree bimorphisms namely (linear an...

Syntax-Directed Translations and Quasi-alphabetic Tree Bimorphisms

Accelerating tree-automatic relations

We study the problem of computing the transitive closure of tree-automatic (binary) relations, which are represented by tree automata. Such relations include classes of infinite systems generated by pushdown systems (PDS), ground tree rewrite systems (GTRS), PA-processes, and Turing machines, to name a few. Although this problem is unsolvable in general, we provide a semi-algorithm for the prob...

Rational tree relations

We investigate forests and relations on trees generated by grammars in which the non-terminals represent relations. This introduces some synchronization between productions. We show that these sets are also solutions of systems of equations, that they are described by rational expressions involving union, substitution and iterated substitution, and that they are preserved by residuals. We show ...