Efficient Inclusion Checking for Deterministic Tree Automata and DTDs

Abstract

Abstract. We present a new algorithm for testing language inclusion L(A) ⊆ L(B) between tree automata in time O(|A| * |B|) where B is deterministic. We extend this algorithm for testing inclusion between automata for unranked trees A and deterministic DTDs D in time O(|A| * |Σ| * |D|). No previous algorithms with these complexities exist.

Equivalence of Deterministic Nested Word to Word Transducers

“…Indeed, taking for example two noncopying and order-preserving dr2w ↑ s S 1 and S 2 over the same domain (otherwise, it just a problem of equivalence over tree automata that can be dealt in O(|S 1 | × |S 2 |), see [3]), one can build two …”

Schema-Guided Induction of Monadic Queries

“…This can be done in time O(|A| * |Σ| * |D|) due to a recent algorithm [6], motivated by the application presented here, which is quite evolved. It avoids quadratic blowups in two places: in the translation of DTDs to bottom-up deterministic tree automata by introducing factorization, and by avoiding automata complementation all over (the completion of a binary tree automaton may be of quadratic size).…”

“…We will use two kinds of schema definitions: XML DTDs and stepwise tree automata [5], possibly with factorization [6] in order to avoid a quadratic blowup when encoding DTDs.…”

“…To avoid such a blowup, we introduce factorized tree automata [6]. These are stepwise tree automata with ǫ-rules which represent stepwise tree automata in a compact manner.…”