Rewrite Closure and CF Hedge Automata

We introduce an extension of hedge automata called bidimensional context-free hedge automata. The class of unranked ordered tree languages they recognize is shown to be preserved by rewrite closure with inverse-monadic rules. We also extend the parameterized rewriting rules used for modeling the W3C XQuery Update Facility in previous works, by the possibility to insert a new parent node above a given node. We show that the rewrite closure of hedge automata languages with these extended rewriting systems are context-free hedge languages

Rewrite based Verification of XML Updates

We consider problems of access control for update of XML documents. In the context of XML programming, types can be viewed as hedge automata, and static type checking amounts to verify that a program always converts valid source documents into also valid output documents. Given a set of update operations we are particularly interested by checking safety properties such as preservation of document types along any sequence of updates. We are also interested by the related policy consistency problem, that is detecting whether a sequence of authorized operations can simulate a forbidden one. We reduce these questions to type checking problems, solved by computing variants of hedge automata characterizing the set of ancestors and descendants of the initial document type for the closure of parameterized rewrite rules

Regular hedge model checking

We extend the regular model checking framework so that it can handle systems with arbitrary width tree-like structures. Con gurations of a system are represented by trees of arbitrary arities, sets of con gurations are represented by regular hedge automata, and the dynamics of a system is modeled by a regular hedge transducer. We consider the problem of computing the transitive closure T + of a regular hedge transducer T. This construction is not possible in general. Therefore, we present a general acceleration technique for computing T+. Our method consists of enhancing the termination of the iterative computation of the different compositions Ti by merging the states of the hedge transducers according to an appropriate equivalence relation that preserves the traces of the transducers. We provide a methodology for effectively deriving equivalence relations that are appropriate. We have successfully applied our technique to compute transitive closures for some mutual exclusion protocols de ned on arbitrary width tree topologies, as well as for an XML application.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

First-order logic for safety verification of hedge rewriting systems

In this paper we deal with verification of safety properties of hedge rewriting systems and their generalizations. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which is further tackled by a generic finite model finding procedure. We show that the proposed approach is at least as powerful as the methods using regular invariants. At the same time the finite countermodel method is shown to be efficient and applicable to the wide range of systems, including the protocols operating on unranked trees

Decidable Classes of Tree Automata Mixing Local and Global Constraints Modulo Flat Theories

We define a class of ranked tree automata TABG generalizing both the tree automata with local tests between brothers of Bogaert and Tison (1992) and with global equality and disequality constraints (TAGED) of Filiot et al. (2007). TABG can test for equality and disequality modulo a given flat equational theory between brother subterms and between subterms whose positions are defined by the states reached during a computation. In particular, TABG can check that all the subterms reaching a given state are distinct. This constraint is related to monadic key constraints for XML documents, meaning that every two distinct positions of a given type have different values. We prove decidability of the emptiness problem for TABG. This solves, in particular, the open question of the decidability of emptiness for TAGED. We further extend our result by allowing global arithmetic constraints for counting the number of occurrences of some state or the number of different equivalence classes of subterms (modulo a given flat equational theory) reaching some state during a computation. We also adapt the model to unranked ordered terms. As a consequence of our results for TABG, we prove the decidability of a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality.Comment: 39 pages, to appear in LMCS journa

Frontiers of tractability for typechecking simple XML transformations

AbstractTypechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type. We focus on complete algorithms which always produce the correct answer. We consider top–down XML transformations incorporating XPath expressions and abstract document types by grammars and tree automata. By restricting schema languages and transformations, we identify several practical settings for which typechecking can be done in polynomial time. Moreover, the resulting framework provides a rather complete picture as we show that most scenarios cannot be enlarged without rendering the typechecking problem intractable. So, the present research sheds light on when to use fast complete algorithms and when to reside to sound but incomplete ones