. Tree patterns are natural candidates for representing rules and hypotheses in many tasks such as information extraction and symbolic mathematics. A tree pattern is a tree with labeled nodes where some of the leaves may be labeled with variables, whereas a tree instance has no variables. A tree pattern matches an instance if there is a consistent substitution for the variables that allows a mapping of subtrees to matching subtrees of the instance. A finite union of tree patterns is called a forest. In this paper, we study the learnability of tree patterns from queries when the subtrees are unordered. The learnability is determined by the semantics of matching as defined by the types of mappings from the pattern subtrees to the instance subtrees. We first show that unordered tree patterns and forests are not exactly learnable from equivalence and subset queries when the mapping between subtrees is one-to-one onto, regardless of the computational power of the learner. Tree and forest pa...

Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with...

Abstract. Many documents such as Web documents or XML files have tree structures. A term tree is an unordered tree pattern consisting of internal variables and tree structures. In order to extract meaningful and hidden knowledge from such tree structured documents, we consider a minimal language (MINL) problem for term trees. The MINL problem for term trees is to find a term tree t such that the language generated by t is minimal among languages, generated by term trees, which contain all given tree structured data. Firstly, we show that the MINL problem for regular term trees is computable in polynomial time if the number of edge labels is infinite. Next, we show that the MINL problems with optimizing the size of an output term tree are NP-complete. Finally, in order to show that our polynomial time algorithm for the MINL problem can be applied to data mining from real-world Web documents, we show that regular term tree languages are polynomial time inductively inferable from positive data if the number of edge labels is infinite. 1

We review topics on formal language aspects of patterns. The main results on the equivalence and inclusion problems are presented. We discuss open problems, in particular, concerning pattern language decision problems and ambiguity in patterns.

We propose a contribution to the PKDD-2002 discovery challenge on the hepatitis dataset. This challenge aims at discovering regularities over patients strucked down by chronic hepatitis. Our approach addresses the problem of multi-relational Data Mining, extracting probabilistic tree patterns from a database using Grammatical Inference techniques.

An algorithm for learning a subclass of erasing regular pattern languages is presented. On extended regular pattern languages generated by patterns π of the form x0α1x1... αmxm, where x0,..., xm are variables and α1,..., αm strings of terminals of length c each, it runs with arbitrarily high probability of success using a number of examples polynomial in m (and exponential in c). It is assumed that m is unknown, but c is known and that samples are randomly drawn according to some distribution, for which we only require that it has certain natural and plausible properties. Aiming to improve this algorithm further we also explore computer simulations of a heuristic.