The theory of tree automata was established in the late sixties by Thatcher and Wright [53] and Doner [19]. They showed that the basic logical and algorithmic properties of standard automata theory can be transferred from the domain of finite words to the domain of finite trees (or terms), leading to a theory of regular tree languages. Quoting from the introduction of [53], where the theory of ...

Current tree parsing algorithms for nonregular tree languages all have superlinear running times, possibly limiting their practical applicability. We present a bottom-up tree automaton that captures exactly the tree-adjoining languages in the non-deterministic case. The determinstic case captures a strict superset of the regular tree languages, while preserving running times linear in the size ...

Tree parsing is an important problem in statistical machine translation. In this context, one is given (a) a synchronous grammar that describes the translation from one language into another and (b) a recognizable set of trees; the aim is to construct a finite representation of the set of those derivations that derive elements from the given set, either on the source side (input restriction) or...

We study tree-automatic linear orders on regular tree languages. We first show that there is no tree-automatic scattered linear order, and in particular no well-order, on the set of all finite labeled trees. This also follows from results of Gurevich-Shelah [8] and Carayol-Löding [4]. We then show that a regular tree language admits a tree-automatic scattered linear order if and only if all tre...

We propose a scheme for the compression of tree structured intermediate code consisting of a sequence of trees specified by a regular tree grammar. The scheme is based on arithmetic coding, and the model that works in conjunction with the coder is automatically generated from the syntactical specification of the tree language. Experiments on data sets consisting of intermediate code trees yield...

We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisf...

This paper investigates the time and space complexity of word order computatio11 ill the psycholinguistically motivated grammar formalism of Performance Gramrnar (PG). In PG, the jirst stage of syntax assembly yields an u11ordered tree (inobile ') co11sisti11g of a hierarchy of lexical f rames (lexically anchored elementary trees). Associated with each lexical frame is a linearizer-a Finite-Sta...

During the last fifteen years, much of the research of proof theoretical grammars has been focused on their weak generative capacity. This research culminated in Pentus’ theorem, which showed that Lambek grammars generate precisely the context-free languages. However, during the same period of time, research on other grammar formalisms has stressed the importance of “strong generative capacity,...

In this paper, we describe a new algorithm for recovering WH-trace empty nodes. Our approach combines a set of hand-written patterns together with a probabilistic model. Because the patterns heavily utilize regular expressions, the pertinent tree structures are covered using a limited number of patterns. The probabilistic model is essentially a probabilistic context-free grammar (PCFG) approach...