17 research outputs found
Learning cover context-free grammars from structural data
We consider the problem of learning an unknown context-free grammar when the
only knowledge available and of interest to the learner is about its structural
descriptions with depth at most The goal is to learn a cover
context-free grammar (CCFG) with respect to , that is, a CFG whose
structural descriptions with depth at most agree with those of the
unknown CFG. We propose an algorithm, called , that efficiently learns
a CCFG using two types of queries: structural equivalence and structural
membership. We show that runs in time polynomial in the number of
states of a minimal deterministic finite cover tree automaton (DCTA) with
respect to . This number is often much smaller than the number of states
of a minimum deterministic finite tree automaton for the structural
descriptions of the unknown grammar
Tree method for quantum vortex dynamics
We present a numerical method to compute the evolution of vortex filaments in
superfluid helium. The method is based on a tree algorithm which considerably
speeds up the calculation of Biot-Savart integrals. We show that the
computational cost scales as Nlog{(N) rather than N squared, where is the
number of discretization points. We test the method and its properties for a
variety of vortex configurations, ranging from simple vortex rings to a
counterflow vortex tangle, and compare results against the Local Induction
Approximation and the exact Biot-Savart law.Comment: 12 pages, 10 figure
Infinitary rewriting: meta-theory and convergence
When infinitary rewriting was introduced by Kaplan et.al. at the beginning of the 1990s, its term universe was explained as the metric completion of a metric on finite terms. The motivation for this connection to topology was that it allowed to import other well-studied notions from metric spaces, in particular the notion of convergence as a replacement for normalisation. This paper generalises the approach by parameterising it with a term metric, and applying the process of metric completion not only to terms but also to operations on and relations between terms. The resulting meta-theory is studied, leading to a revised notion of infinitary rewrite system. For these systems a method is devised to prove their convergence
Learning a Regular Tree Language From a Teacher
We generalize an inference algorithm by Angluin, that learns a regular string language from a "minimally adequate teacher", to regular tree languages. This improves a similar algorithm proposed by Sakakibara. In particula
Locating Matches of Tree Patterns in Forests
. We deal with matching and locating of patterns in forests of variable arity. A pattern consists of a structural and a contextual condition for subtrees of a forest, both of which are given as tree or forest regular languages. We use the notation of constraint systems to uniformly specify both kinds of conditions. In order to implement pattern matching we introduce the class of pushdown forest automata. We identify a special class of contexts such that not only pattern matching but also locating all of a forest's subtrees matching in context can be performed in a single traversal. We also give a method for computing the reachable states of an automaton in order to minimize the size of transition tables. 1 Introduction In Standard Generalized Markup Language (SGML) [Gol90] documents are represented as trees. A node in a document tree may have arbitrarily many children, independent of the symbol at that node. A sequence of documents or subdocuments is called a forest. A main task in do..