This paper describes the precise speci cation, design, analysis, implementation, and measurements of an e cient algorithm for solving regular tree grammar based constraints. The particular constraints are for dead-code elimination on recursive data, but the method used for the algorithm design and complexity analysis is general and applies to other program analysis problems as well. The method ...

Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly b children, with b ≥ 3. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the root. Notice that it is still unknown if vertexreinforced jump process is transient on the binary tree.

We present a formal framework that generalizes a variety of monolingual and synchronous grammar formalisms for parsing and translation. Our framework is based on regular tree grammars that describe derivation trees, which are interpreted in arbitrary algebras. We obtain generic parsing algorithms by exploiting closure properties of regular tree languages.

The use of regular tree grammars to represent and build models of formulae of rst-order logic without equality is investigated. The combination of regular tree grammars with equational constraints provides a powerful and general way of representing Herbrand models. We show that the evaluation problem (i.e. the problem of nding the truth value of a formula in a given model) is decidable when mod...

Pebble tree-walking automata with alternation were first investigated by Milo, Suciu and Vianu (2003), who showed that tree languages recognized by these devices are exactly the regular tree languages. We strengthen this by proving the same result for pebble automata with “strong pebble handling” which means that pebbles can be lifted independently of the position of the reading head and withou...

A regular tree language L is locally testable if membership of a tree in L depends only on the presence or absence of some fix set of neighborhoods in the tree. In this paper we show that it is decidable whether a regular tree language is locally testable. The decidability is shown for ranked trees and for unranked unordered trees.

Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly b children, with b ≥ 3. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the root. Notice that it is still unknown if vertex-reinforced jump process is transient on the binary tree. Dipartimento di Matematica applicata, Università Ca’ Fosc...

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 weighted tree language, which is a mapping from the set of trees to the multioperator monoid. We prove that, for multioperator monoids canonically associated to par...

Tree languages are powerful tools for the representation and schematization of infinite sets of terms for various purposes (unification theory, verification and specification ...). In order to extend the regular tree language framework, more complex formalisms have been developed. In this paper, we focus on Tree Synchronized Grammars and Primal Grammars which introduce specific control structur...

We generalise Constrained Dynamic Pushdown Networks, introduced by Bouajjani et al., to Constrained Dynamic Tree Networks. In this model, we have trees of processes which may monitor their children. We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable. We address the problem of symbolic reachability analysis for this model. Mo...