Minimizing Tree Automata for Unranked Trees
نویسندگان
چکیده
Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottomup determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are not unique and that minimization is np-hard. We then study more recent automata classes that do allow for polynomial time minimization. Among those, we show that bottom-up deterministic stepwise tree automata yield the most succinct representations.
منابع مشابه
Equivalences between Ranked and Unranked Weighted Tree Automata via Binarization
Encoding unranked trees to binary trees, henceforth called binarization, is an important method to deal with unranked trees. For each of three binarizations we show that weighted (ranked) tree automata together with the binarization are equivalent to weighted unranked tree automata; even in the probabilistic case. This allows to easily adapt training methods for weighted (ranked) tree automata ...
متن کاملSeries, Weighted Automata, Probabilistic Automata and Probability Distributions for Unranked Trees
We study tree series and weighted tree automata over unranked trees. The message is that recognizable tree series for unranked trees can be defined and studied from recognizable tree series for binary representations of unranked trees. For this we prove results of [1] as follows. We extend hedge automata – a class of tree automata for unranked trees – to weighted hedge automata. We define weigh...
متن کاملOn the minimization of XML Schemas and tree automata for unranked trees
Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. First, we study unranked tree automata that are standard in database theory, assuming bottom-up determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal automata in that class are not u...
متن کاملQuerying Unranked Trees with Stepwise Tree Automata
The problem of selecting nodes in unranked trees is the most basic querying problem for XML. We propose stepwise tree automata for querying unranked trees. Stepwise tree automata can express the same monadic queries as monadic Datalog and monadic second-order logic. We prove this result by reduction to the ranked case, via a new systematic correspondence that relates unranked and ranked queries.
متن کاملFinite automata on unranked trees: extensions by arithmetical and equality constraints
The notion of unranked trees has attracted much interest in current research, especially due to their application as formal models of XML documents. In particular, several automata and logic formalisms on unranked trees have been considered (again) in the literature, and many results that had previously been shown for the ranked-tree setting have turned out to hold for the unranked-tree setting...
متن کامل