In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued)  regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is ta...

In this thesis, three methods are investigated to express context-free tree languages by regular tree grammars. The first method is a characterization. We show restrictions to context-free tree grammars such that, for each restricted context-free tree grammar, a regular tree grammar can be constructed that induces the same tree language. The other two methods are approximations. An arbitrary co...

This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two problems that are crucial for many applications of tree automata. For size reduction of tree automata, we adapt the simulation quotient technique that is well...

In this paper we lift the result of Hashiguchi of decidability of the restricted star-height problem for words to the level of finite trees. Formally, we show that it is decidable, given a regular tree language L and a natural number k whether L can be described by a disjunctive μ-calculus formula with at most k nesting of fixpoints. We show the same result for disjunctive μ-formulas allowing s...

In this master thesis project a class of tree grammars called “Branching tree grammar” has been implemented into the TREEBAG system. A tree grammar is a device that generates a language of mathematical trees, according to rules specified by the user. These trees can then be transformed into for example pictures, by other components in TREEBAG. The branching tree grammar, which is a class of gra...

Weakly definable languages of infinite trees are an expressive subclass of regular tree languages definable in terms of weak monadic second-order logic, or equivalently weak alternating automata. Our main result is that given a Büchi automaton, it is decidable whether the language is weakly definable. We also show that given a parity automaton, it is decidable whether the language is recognizab...

Static analysis of programs using regular tree grammars has been studied for more than 30 years, the earliest example being Reynolds’ work on automatic derivation of data-type definitions from untyped functional programs. Recently the topic has attracted renewed attention, with applications in program specialisation, data flow analysis, shape analysis, mode and type inference, termination analy...

The field of finite tree automata provides fundamental notations and tools for reasoning about set of terms called regular or recognizable tree languages. We consider two kinds of analysis using regular tree languages, applied to logic programs. The first approach is to try to discover automatically a tree automaton from a logic program, approximating its minimal Herbrand model. In this case th...

We define tree insertion systems which generates trees. The generative power is compared with the traditional generating and accepting devices for trees. Methods for conversion of tree insertion system to regular tree grammar and finite state bottom-up tree automata to tree insertion system are expalined with suitable examples. An outline of proof by induction for the equivalence of tree insert...

A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific simple trees and a structure is word automatic if it is encodable using only these trees. The question naturally arises whether a given tree automatic structure i...