Schema design for XML repositories

Abstract

Abiteboul et al. initiated the systematic study of distributed XML documents consisting of several logical parts, possibly located on different machines. The physical distribution of such documents immediately raises the following question: how can a global schema for the distributed document be broken up into local schemas for the different logical parts? The desired set of local schemas should guarantee that, if each logical part satisfies its local schema, then the distributed document satisfies the global schema.Abiteboul et al. proposed three levels of desirability for local schemas: local typing, maximal local typing, and perfect local typing. Immediate algorithmic questions are: (i) given a typing, determine whether it is local, maximal local, or perfect, and (ii) given a document and a schema, establish whether a (maximal) local or perfect typing exists. This paper improves the open complexity results in their work and initiates the study of (i) and (ii) for schema restrictions arising from the current standards: DTDs and XML Schemas with deterministic content models. The most striking result is that these restrictions yield tractable complexities for the perfect typing problem.Furthermore, an open problem in Formal Language Theory is settled: deciding language primality for deterministic finite automata is pspace-complete.

On simplification of schema mappings

“…Taking into account the language-theoretic view, our work has also connections with [39,40], which also study language constraints of the forms e 1 e 2 , and e 1 = e 2 . However, in these works, e 1 is restricted to be a single word on both the source and the target alphabets.…”

“…Our technique for mapping simplification exploits a characterization of regular languages by means of congruence classes [49,50,40]. Recall that two words u, v ∈ Σ * are congruent with respect to a language L ⊆ Σ * if, for all words x, y ∈ Σ * we have that xu y ∈ L iff xv y ∈ L. Let A t = (Σ t , S t , s 0 t , δ t , F t ) be a 1NFA for q t .…”

Simplifying schema mappings

“…The key idea of our approach is that we can prove that solutions of the above equations are closed under congruence, which enables us to represent languages as graphs over the finite-state automaton for e2. Taking into account the language-theoretic view, our work has also connections with [4,42], which also study language constraints of the forms e1 e2, and e1 = e2. However, in these works, e1 is restricted to be a single word on both the source and the target alphabets.…”

On Language Equations with One-sided Concatenation

“…This topic was further studied in the monographs on algebraic automata theory by Salomaa [34] and Conway [12]. There has been a renewed interest in the topic over the last two decades, with the state-of-the-art as of 2007 presented in a survey by Kunc [19], and with more research on various aspects of language equations appearing in the last few years [13,16,17,20,22,30].As an example, consider the equation X = AX ∪ B, where A, B are fixed formal languages. It is well-known, that this equation has A * B as a solution.…”

“…. , X n ) = const, studied by Bala [7], where the solution existence problem is EXPSPACE-hard, while the special case XY = const was proved to be PSPACE-complete by Martens et al [22]. Another example is given by resolved systems of equations with concatenation and complementation, investigated by Okhotin and Yakimova [31], which have NP-complete solvability testing.…”