A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular, decidability of the problem whether a given language is recognisable by some unambiguous automaton is open. Moreover, there are no known upper bounds on the descript...

There exist several methods of computing an automaton recognizing the language denoted by a given regular expression: In the case of words, ones can compute the position automaton P due to Glushkov, the c-continuation automaton C due to Champarnaud and Ziadi, the follow automaton F due to Illie and Yu and the equation automaton E due to Antimirov. It has been shown that P and C are isomorphic a...

The following problem is shown undecidable: given regular languages L,K of finite trees, decide if there exists a deterministic tree-walking automaton which accepts all trees in L and rejects all trees in K. The proof uses a technique of Kopczyński from [Kop].

The word position automaton was introduced by Glushkov and McNaughton in the early 1960. This automaton is homogeneous and has (||E || + 1) states for a word expression of alphabetic width ||E ||. This kind of automata is extended to regular tree expressions. In this paper, we give an efficient algorithm that computes the Follow sets, which are used in different algorithms of conversion of a re...

Feature-based regular tree grammars (FRTG) can be used to generate the derivation trees of a featurebased tree adjoining grammar (FTAG). We make use of this fact to specify and implement both an FTAG-based sentence realiser and a benchmark generator for this realiser. We argue furthermore that the FRTG encoding enables us to improve on other proposals based on a grammar of TAG derivation trees ...

In this paper, we propose a two fold generic parser. First, it simulates the behavior of multiple parsing automata. Second, it parses strings drawn from either a context free grammar, a regular tree grammar, or from both. The proposed parser is based on an approach that defines an extended version of an automaton, called positionparsing automaton (PPA) using concepts from LR and regular tree au...

We derive performance measures for burst arrival (e.g. messages of variable length packets) M / G / 1 queues with server vacations, controlled by the, so called, Randomly Timed Gated (RTG) protocol, operating as follows : Whenever the server returns from a ( general-type ) vacation and initiates a busy period, a Timer with random duration T is activated. If the server empties the queue before t...

We consider a simple model of transport on a regular tree, whereby species evolve according to the drift-diffusion equation, and the drift velocity on each branch of the tree is a quenched random variable. The inverse of the steady-state amplitude at the origin is expressed in terms of a random geometric series whose convergence or otherwise determines whether the system is localized or delocal...

We introduce a new geometric tool for analyzing groups of finite au-tomata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reproduc...

Millstream systems have recently been proposed as a formalization of the linguistic idea that natural language should be described as a combination of different modules related by interfaces. In this paper we investigate algorithmic properties of Millstream systems having regular tree grammars as modules and MSO logic as interface logic. We focus on the so-called completion problem: Given trees...