Related papers: The Wadge Hierarchy of Deterministic Tree Language…
We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindstr\"om quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization…
Trees -- i.e., the type of data structure known under this name -- are central to many aspects of knowledge organization. We investigate some central design choices concerning the ontological modeling of such trees. In particular, we…
We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the…
We consider the two-variable fragment FO^2[<] of first-order logic over finite words. Numerous characterizations of this class are known. Th\'erien and Wilke have shown that it is decidable whether a given regular language is definable in…
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…
We study the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that every pair of disjoint WSTS languages is regularly separable: there is a regular language…
Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second-order theory of certain structures. More recently, these descriptive…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
It is well known that for a given bottom-up tree automaton it can be decided whether or not there exists deterministic top-down tree automaton that recognized the same tree language. Recently it was claimed that such a decision can be…
A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word…
An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if it is…
We prove some results on the Wadge order on the space of sets of natural numbers endowed with Scott topology, and more generally, on omega-continuous domains. Using alternating decreasing chains we characterize the property of Wadge…
The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that…
We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…
We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into…
We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation is definable (1)~by a linear top-down tree transducer or (2)~by a tree homomorphism. We present algorithms that…
We study a class of algebras that can be used as recognisers for regular languages of infinite trees.
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
Similar to a tree grammar, a Horn theory can be used to describe an infinite set of terms. In this paper, we present a class of Horn theories such that the set of definable predicates is closed wrt. conjunction and such that the…
We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma…