For the class of linear context-free tree grammars, we define a decidable property called self-embedding. We prove that each non-self-embedding grammar in this class generates a regular tree language and show how to construct the equivalent regular tree grammar.

We study the edit-distance of regular tree languages. The edit-distance is a metric for measuring the similarity or dissimilarity between two objects, and a regular tree language is a set of trees accepted by a finite-state tree automaton or described by a regular tree grammar. Given two regular tree languages L and R, we define the editdistance d(L,R) between L and R to be the minimum edit-dis...

We extend the automata-theoretic framework for reasoning about infinitestate sequential systems to handle also the global model-checking problem. 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. Chec...

An algorithm to decide inclusion for languages de ned by deterministic regular tree grammars is presented. The algorithm is shown to run in polynomial time based on the number of constructors, constructor arity, and number of non-terminals. Correctness proofs are included. 1 Regular tree grammars A regular tree grammar, G, is a grammar for constructing trees. Formally, G = (C;N;P; S) where: 1. ...

We consider a graph G and a covering G̃ of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite k-regular tree and we examine the heat kernels for general k-regular graphs. In particular, we show that a k-regular graph on n vertices has at most (1 + o(1)) 2 log n kn log k (k − 1)k−1 (k2 − 2k)k/2−1 n spanning trees, which is best possible...

We show that it is decidable whether a given a regular tree language belongs to the class ∆2 of the Borel hierarchy, or equivalently whether the Wadge degree of a regular tree language is countable.

In this paper we extend the work by Michaelis (1999) which shows how to encode an arbitrary Minimalist Grammar in the sense of Stabler (1997) into a weakly equivalent multiple contextfree grammar (MCFG). By viewing MCFG-rules as terms in a free Lawvere theory we can translate a given MCFG into a regular tree grammar. The latter is characterizable by both a tree automaton and a corresponding for...

This paper describes a new representation for sortal constraints and a uniication algorithm for the corresponding constrained terms. Variables range over sets of terms described by systems of set constraints that can express limited inter-variable dependencies. These sets of terms are more general than regular tree languages, but are still closed under intersection. The new uniication algorithm...

Three closely related proposals for adding (cyclic) adjunction to Minimalist grammars are given model-theoretic definitions and investigated with respect to their linguistic and formal properties. While they differ with respect to their linguistic adequacy, they behave largely the same on a computational level. Weak generative capacity is not affected, and while subregular complexity varies bet...

Since recognizable tree languages are closed under the rational operations, every regular tree expression denotes a recognizable tree language. We provide an alternative proof to this fact that results in smaller tree automata. To this aim, we transfer Antimirov’s partial derivatives from regular word expressions to regular tree expressions. For an analysis of the size of the resulting automato...