Views and queries: Determinacy and rewriting

We investigate the question of whether a query Q can be answered using a set V of views. We first define the problem in information-theoretic terms: we say that V determines Q if V provides enough information to uniquely determine the answer to Q. Next, we look at the problem of rewriting Q in terms of V using a specific language. Given a view language V and query language Q, we say that a rewriting language R is complete for Vto-Q rewritings if every Q ε Q can be rewritten in terms of V ε v using a query in R, whenever V determines Q. While query rewriting using views has been extensively investigated for some specific languages, the connection to the information-theoretic notion of determinacy, and the question of completeness of a rewriting language, have received little attention. In this paper we investigate systematically the notion of determinacy and its connection to rewriting. The results concern decidability of determinacy for various view and query languages, as well as the power required of complete rewriting languages. We consider languages ranging from first-order to conjunctive queries.

[1]  William Craig,et al.  Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory , 1957, Journal of Symbolic Logic.

[2]  Anand Rajaraman,et al.  Conjunctive query containment revisited , 1997, Theor. Comput. Sci..

[3]  Martin Otto,et al.  An Interpolation Theorem , 2000, Bulletin of Symbolic Logic.

[4]  C. Earle,et al.  On the Moduli of Closed Riemann Surfaces with Symmetries , 1971 .

[5]  Georg Gottlob,et al.  Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width , 2003, J. Comput. Syst. Sci..

[6]  Leila Schneps,et al.  Geometric Galois Actions: 2. The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups , 1997 .

[7]  Georg Gottlob,et al.  Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width , 2001, PODS '01.

[8]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.

[9]  Zoé Lacroix,et al.  Generalized Implicit Definitions on Finite Structures , 1995, CSL.

[10]  M. Streit,et al.  Homology, Belyî functions and canonical curves , 1996 .

[11]  Diego Calvanese,et al.  Rewriting of regular expressions and regular path queries , 1999, PODS '99.

[12]  Yannis Papakonstantinou,et al.  Describing and Using Query Capabilities of Heterogeneous Sources , 1997, VLDB.

[13]  Armand Borel,et al.  Commensurability classes and volumes of hyperbolic 3-manifolds , 1981 .

[14]  G. Belyi.  On Galois Extensions of a Maximal Cyclotomic Field , 1980 .

[15]  Jean-Pierre Chauveau,et al.  Esquisse d'un programme , 1982 .

[16]  A. Weil,et al.  The Field of Definition of a Variety , 1956 .

[17]  Jan Van den Bussche,et al.  The Semijoin Algebra and the Guarded Fragment , 2004, J. Log. Lang. Inf..

[18]  Alin Deutsch,et al.  Physical Data Independence, Constraints, and Optimization with Universal Plans , 1999, VLDB.

[19]  Jürgen Wolfart,et al.  Characters and galois invariants of regular dessins , 2000 .

[20]  Steven Lindell.  The logical complexity of queries on unordered graphs , 1987 .

[21]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[22]  Yuri Gurevich,et al.  The Classical Decision Problem , 1997, Perspectives in Mathematical Logic.

[23]  Jeffrey D. Ullman,et al.  Information integration using logical views , 1997, Theor. Comput. Sci..

[24]  P. Beazley Cohen,et al.  Dessins de Grothendieck et variétés de Shimura , 1992 .

[25]  Y. Gurevich.  On Finite Model Theory , 1990 .

[26]  Divesh Srivastava,et al.  Answering Queries Using Views. , 1999, PODS 1995.

[27]  Stéphane Grumbach,et al.  On the content of materialized aggregate views , 2000, PODS '00.

[28]  Surajit Chaudhuri,et al.  Automated Selection of Materialized Views and Indexes in SQL Databases , 2000, VLDB.

[29]  Per-Åke Larson,et al.  Query Transformation for PSJ-Queries , 1987, VLDB.

[30]  Jürgen Wolfart,et al.  Geometric Galois Actions: The ‘obvious’ part of Belyi's theorem and Riemann surfaces with many automorphisms , 1997 .

[31]  A. Clebsch,et al.  Theorie der Abelschen functionen , 1967 .

[32]  Jeffrey D. Ullman,et al.  Answering queries using templates with binding patterns (extended abstract) , 1995, PODS '95.

[33]  Diego Calvanese,et al.  View-based query processing for regular path queries with inverse , 2000, PODS '00.

[34]  Divesh Srivastava,et al.  Semantic Data Caching and Replacement , 1996, VLDB.

[35]  Anand Rajaraman,et al.  Answering queries using templates with binding patterns (extended abstract) , 1995, PODS.

[36]  Serge Abiteboul,et al.  Complexity of answering queries using materialized views , 1998, PODS.

[37]  Erich Grädel,et al.  On the Restraining Power of Guards , 1999, Journal of Symbolic Logic.

[38]  P. Dèbes,et al.  On fields of moduli of curves , 1999 .

[39]  Goro Shimura.  On the field of rationality for an abelian variety , 1972 .

[40]  Nicolas Spyratos,et al.  Update semantics of relational views , 1981, TODS.

[41]  A. Tarski.  Einige methodologifche Unterfuchungen über die Definierbarkeit der Begriffe , 1935 .

[42]  Michael R. Genesereth,et al.  Answering recursive queries using views , 1997, PODS '97.

[43]  Toru Komatsu,et al.  Geometric balance of cuspidal points realizing dessins d'enfants on the Riemann sphere , 2001 .

[44]  Leila Schneps,et al.  The Grothendieck theory of dessins d'enfants , 1994 .

[45]  Foto N. Afrati,et al.  Rewriting Conjunctive Queries Determined by Views , 2007, MFCS.

[46]  B. Sadi,et al.  Descente effective du corps de définition des revêtements galoisiens , 1999 .

[47]  G. Jones,et al.  Belyi Functions, Hypermaps and Galois Groups , 1996 .

[48]  Evert W. Beth,et al.  On Padoa’s Method in the Theory of Definition , 1953 .

[49]  Alan Nash,et al.  Determinacy and Rewriting of Conjunctive Queries Using Views: A Progress Report , 2007, ICDT.

[50]  Diego Calvanese,et al.  Lossless regular views , 2002, PODS.

[51]  Chen Li,et al.  Answering queries using views with arithmetic comparisons , 2002, PODS '02.

[52]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[53]  Emil L. Post.  Recursive Unsolvability of a problem of Thue , 1947, Journal of Symbolic Logic.

[54]  G. Jones,et al.  Galois groups, monodromy groups and cartographic groups , 1997 .

[55]  Maurizio Rafanelli,et al.  Querying aggregate data , 1999, PODS '99.

[56]  Maarten Marx,et al.  Queries determined by views: pack your views , 2007, PODS.

[57]  Jürgen Wolfart,et al.  Fuchsian triangle groups and Grothendieck dessins. Variations on a theme of Belyi , 1994 .

[58]  G. Belyi,et al.  Another proof of the three points theorem , 2002 .

[59]  Kevin R. Coombes,et al.  Hurwitz families and arithmetic Galois groups , 1985 .

[60]  G. Jones,et al.  Theory of Maps on Orientable Surfaces , 1978 .

[61]  S. Kleene.  Review: Emil L. Post, Recursive Unsolvability of a Problem of Thue , 1947 .

[62]  Leonid Libkin,et al.  Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series) , 2004 .

[63]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.