For a given binary relation of finite trees, we consider the synthesis problem of deciding whether there is a deterministic top-down tree transducer that uniformizes the relation, and constructing such a transducer if it exists. A uniformization of a relation is a function that is contained in the relation and has the same domain as the relation. It is known that this problem is decidable if th...

It is known that by iterating the look-ahead tree languages for deterministic topdown tree automata, more and more powerful recognizing devices are obtained. Let DR0 = DR, where DR is the class of all tree languages recognizable by deterministic top-down tree automata, and let, for n 1, DRn be the class of all tree languages recognizable by deterministic top-down tree automata with DRn 1 lookah...

We introduce various types of w-automata, top-down automata and bottom-up automata on infinite trees. We study the power of deterministic and nondeter-ministic tree automata and prove that deterministic and non-deterministic bottom-up tree automata accept the same intinite tree sets. We establish a relationship between tree automata, Logic programs, recursive program schemes, and the monadic se...

In strong contrast to their non-deterministic counterparts, deterministic top-down tree automata received little attention in the scientific literature. The aim of this article is to survey recent and less recent results and stipulate new research directions for top-down deterministic tree automata motivated by the advent of the XML data exchange format. In particular, we survey different ranke...

We present algorithms for testing language inclusion L(A) ⊆ L(B) between tree automata in time O(|A| · |B|) where B is deterministic (bottom-up or top-down). We extend our algorithms for testing inclusion of automata for unranked trees A in deterministic DTDs or deterministic EDTDs with restrained competition D in time O(|A| · |Σ| · |D|). Previous algorithms were less efficient or less general.

A recent minimization technique, called hyper-minimization, permits reductions of language representations beyond the limits imposed by classical semantics-preserving minimization. Naturally, the semantics is not preserved by hyper-minimization; rather the reduced representation, which is called hyper-minimal, can accept a language that has a nite symmetric di erence to the language of the orig...

In this paper, we address the problem of reducing the size of nondeterministic (bottom-up) tree automata. We propose a uniform framework that allows for combining various upward and downward bisimulation and simulation relations in order to obtain a language-preserving combined relation suitable for reducing tree automata without a need to determinise them. The framework generalises and improve...

This paper discusses the decidability of node query preservation problems for XML document transformations. We assume a transformation given by a deterministic linear top-down data tree transducer (abbreviated as DLTV ) and an n-ary query based on runs of a tree automaton. We say that a DLTV Tr strongly preserves a query Q if there is a query Q′ such that for every document t, the answer set of...