This paper proposes an extension to the formalism of regular expressions with a form of predicate logic where quantified propositions apply to substrings. The implementation hinges crucially on the manipulation of auxiliary symbols which has been a common, though previously unsystematized practice in finitestate language processing. We also apply the notation to give alternate compilation metho...

We introduce the notion of regular cost functions: a quantitative extension to the standard theory of regular languages. We provide equivalent characterisations of this notion by means of automata (extending the nested distance desert automata of Kirsten), of history-deterministic automata (history-determinism is a weakening of the standard notion of determinism, that replaces it in this contex...

We show that the set of all formulas in n variables valid in a finite class A of finite algebras is always a regular tree language, and compute a finite axiom set for A. We give a rational reconstruction of Barzdins’ liquid flow algorithm [BB91]. We show a sufficient condition for the existence of a class A of prototype algebras for a given theory Θ. Such a set allows us to prove Θ |= φ simply ...

The identification and representation of building roof topology are basic, but important, issues for 3D building model reconstruction from point clouds. Always, the roof topology is expressed by the roof topology graph (RTG), which stores the plane–plane adjacencies as graph edges. As the decision of the graph edges is often based on local statistics between adjacent planes, topology errors can...

A set of (labeled) graphs can be de ned by a regular tree language and one regular string language for each possible edge label, as follows. For each tree t from the regular tree language the graph gr(t) has the same nodes as t (with the same labels), and there is an edge with label from node x to node y if the string of labels of the nodes on the shortest path from x to y in t belongs to the r...

Restricting the input or the output of a grammar-induced translation to a given set of trees plays an important role in statistical machine translation. The problem for practical systems is to find a compact (and in particular, finite) representation of said restriction. For the class of synchronous treeadjoining grammars, partial solutions to this problem have been described, some being restri...

One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this problem and similar ones using the language of universal algebra, highlighting potential connections to the structural theory of finite algebras, including Tame...

We deene a new class of automata which is an acceptor model for mappings from the set of terms T over a ranked alphabet into a set E of labels. When E = f0; 1g n an automaton can be viewed as an acceptor model for n-tuples of tree languages. We prove decidability of emptiness and closure properties for this class of automata. As a consequence of these results, we prove decidability of satissabi...

We propose a set of transformation rules for rst order formulae whose atoms are either equations between terms or \membership constraints" t 2. can be interpreted as a regular tree language (is called a sort in the algebraic speciication community) or as a tree language in any class of languages which satisses some adequate closure and decidability properties. This set of rules is proved to be ...

The main result of this paper is a description of linguisticallymotivated non-contextfree phenomena equivalently in terms of regular tree languages (to express the recursive properties) and both a logical and an operational perspective (to establish the intended linguistic relations). The result is exemplified with a particular noncontext-free phenomenon, namely cross-serial dependencies in nat...