An Automata-Theoretic Approach to

In this paper we present Regular XPath (RXPath), which is a natural extension of XPath with regular expressions over paths that has the same computational properties as XPath: linear-time query eval- uation and exponential-time reasoning. To establish these results, we de- vise a unifying automata-theoretic framework based on two-way weak alternating tree automata. Specifically, we consider automata that have infinite runs on finite trees. This enables us to leverage and simplify existing automata-theoretic machinery and develop algorithms both for query evaluation and for reasoning over queries. With respect to the lat- ter problem, we consider RXPath as a constraint language, and study constraint satisfiability, and query satisfiability and containment under constraints in the setting of RXPath.

[1]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[2]  Giora Slutzki,et al.  Alternating Tree Automata , 1983, Theor. Comput. Sci..

[3]  Joost Engelfriet,et al.  Macro Tree Transducers , 1985, J. Comput. Syst. Sci..

[4]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[5]  David J. Weir,et al.  Characterizing Structural Descriptions Produced by Various Grammatical Formalisms , 1987, ACL.

[6]  Haim Gaifman,et al.  Decidable optimization problems for database logic programs , 1988, STOC '88.

[7]  Stuart M. Shieber,et al.  Synchronous Tree-Adjoining Grammars , 1990, COLING.

[8]  Tadao Kasami,et al.  On Multiple Context-Free Grammars , 1991, Theor. Comput. Sci..

[9]  Noam Chomsky,et al.  The Minimalist Program , 1992 .

[10]  Joost Engelfriet,et al.  Graph Grammars and Tree Transducers , 1994, CAAP.

[11]  S. Shieber RESTRICTING THE WEAK‐GENERATIVE CAPACITY OF SYNCHRONOUS TREE‐ADJOINING GRAMMARS , 1994, Comput. Intell..

[12]  Edward P. Stabler,et al.  Derivational Minimalism , 1996, LACL.

[13]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[14]  Jens Michaelis,et al.  Derivational Minimalism Is Mildly Context-Sensitive , 1998, LACL.

[15]  Moshe Y. Vardi Reasoning about The Past with Two-Way Automata , 1998, ICALP.

[16]  Joost Engelfriet,et al.  Tree Languages Generated be Context-Free Graph Grammars , 1998, TAGT.

[17]  Diego Calvanese,et al.  Representing and Reasoning on XML Documents: A Description Logic Approach , 1999, J. Log. Comput..

[18]  Joost Engelfriet,et al.  Macro Tree Transducers, Attribute Grammars, and MSO Definable Tree Translations , 1999, Inf. Comput..

[19]  Jonathan Bobaliik Adverbs:The Hierarchy Paradox. , 1999 .

[20]  Pierre Wolper,et al.  An automata-theoretic approach to branching-time model checking , 2000, JACM.

[21]  Marcin Jurdzinski,et al.  Small Progress Measures for Solving Parity Games , 2000, STACS.

[22]  Ulrike Sattler,et al.  The Hybrid µ-Calculus , 2001, IJCAR.

[23]  J. Michaelis,et al.  On Minimalist Attribute Grammars and Macro Tree Transducers , 2001 .

[24]  Diego Calvanese,et al.  View-Based Query Answering and Query Containment over Semistructured Data , 2001, DBPL.

[25]  Diego Calvanese,et al.  Reasoning on regular path queries , 2003, SGMD.

[26]  Edward P. Stabler,et al.  Structural similarity within and among languages , 2003, Theor. Comput. Sci..

[27]  Frank Neven,et al.  DTDs versus XML schema: a practical study , 2004, WebDB '04.

[28]  Zoltán Fülöp,et al.  A bottom-up characterization of deterministic top-down tree transducers with regular look-ahead , 2004, Inf. Process. Lett..

[29]  Maarten Marx,et al.  XPath with Conditional Axis Relations , 2004, EDBT.

[30]  Thomas Schwentick,et al.  XPath query containment , 2004, SGMD.

[31]  G. Gottlob,et al.  Efficient algorithms for processing XPath queries , 2002, TODS.

[32]  Maarten Marx,et al.  First Order Paths in Ordered Trees , 2005, ICDT.

[33]  Zoltán Fülöp,et al.  Linear deterministic multi bottom-up tree transducers , 2005, Theor. Comput. Sci..

[34]  Wenfei Fan,et al.  XML constraints: specification, analysis, and applications , 2005, 16th International Workshop on Database and Expert Systems Applications (DEXA'05).

[35]  Joost Engelfriet,et al.  Context-free hypergraph grammars have the same term-generating power as attribute grammars , 1992, Acta Informatica.

[36]  Joost Engelfriet,et al.  Top-down tree transducers with regular look-ahead , 1975, Mathematical systems theory.

[37]  M. de Rijke,et al.  PDL for ordered trees , 2005, J. Appl. Non Class. Logics.

[38]  Wolfgang Thomas,et al.  Observations on determinization of Büchi automata , 2006, Theor. Comput. Sci..

[39]  Stuart M. Shieber,et al.  Simpler TAG semantics through synchronization , 2006 .

[40]  Stuart M. Shieber Unifying Synchronous Tree Adjoining Grammars and Tree Transducers via Bimorphisms , 2006, EACL.

[41]  Michael Pan Pomset mcfgs , 2007, IWPT.

[42]  Wenfei Fan,et al.  Rewriting Regular XPath Queries on XML Views , 2007, 2007 IEEE 23rd International Conference on Data Engineering.

[43]  Pierre Genevès,et al.  Efficient static analysis of XML paths and types , 2007, PLDI '07.

[44]  Mikolaj Bojanczyk,et al.  XPath evaluation in linear time , 2008, PODS.

[45]  Balder ten Cate,et al.  XPath, transitive closure logic, and nested tree walking automata , 2008, PODS.

[46]  Jens Michaelis An Additional Observation on Strict Derivational Minimalism , 2009 .

[47]  Cristina Sirangelo,et al.  Reasoning about XML with temporal logics and automata , 2010, J. Appl. Log..