Related papers: Piecewise testable tree languages
We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
It has been argued that, when learning a first language, babies use a series of small clues to aid recognition and comprehension, and that one of these clues is word length. In this paper we present a statistical part of speech tagger which…
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…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…
The task of text segmentation may be undertaken at many levels in text analysis---paragraphs, sentences, words, or even letters. Here, we focus on a relatively fine scale of segmentation, hypothesizing it to be in accord with a stochastic…
We introduce a graph polynomial that distinguishes tree structures to represent dependency grammar and a measure based on the polynomial representation to quantify syntax similarity. The polynomial encodes accurate and comprehensive…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics. These include the temporal logics CTL and EF, and first-order logic over…
Commutative languages with the semilinear property (SLIP) can be naturally recognized by real-time NLOG-SPACE multi-counter machines. We show that unions and concatenations of such languages can be similarly recognized, relying on -- and…
Characterisations theorems serve as important tools in model theory and can be used to assess and compare the expressive power of temporal languages used for the specification and verification of properties in formal methods. While complete…
Sturmian words are infinite binary words with many equivalent definitions: They have a minimal factor complexity among all aperiodic sequences; they are balanced sequences (the labels 0 and 1 are as evenly distributed as possible) and they…
Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual…
We introduce weighted regular tree grammars with storage as combination of (a) regular tree grammars with storage and (b) weighted tree automata over multioperator monoids. Each weighted regular tree grammar with storage generates a…
In data languages the positions of strings and trees carry a label from a finite alphabet and a data value from an infinite alphabet. Extensions of automata and logics over finite alphabets have been defined to recognize data languages,…
The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…
Computation Tree Logic (CTL) and its extensions CTL* and CTL+ are widely used in automated verification as a basis for common model checking tools. But while they can express many properties of interest like reachability, even simple…
A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular…
For which unary predicates $P_1, \ldots, P_m$ is the MSO theory of the structure $\langle \mathbb{N}; <, P_1, \ldots, P_m \rangle$ decidable? We survey the state of the art, leading us to investigate combinatorial properties of…