Real Algebraic Geometry and Constraint Databases

[1]  Operational Semantics for Fixed-Point Logics on Constraint Databases , 2001, LPAR.

[2]  Michael Benedikt,et al.  Languages for relational databases over interpreted structures , 1997, PODS '97.

[3]  S. Basu,et al.  Algorithms in real algebraic geometry , 2003 .

[4]  Floris Geerts Expressing the box cone radius in the relational calculus with real polynomial constraints , 2003, Discret. Comput. Geom..

[5]  Jan Van den Bussche,et al.  Topological elementary equivalence of closed semi-algebraic sets in the real plane , 2000, Journal of Symbolic Logic.

[6]  Gabriel M. Kuper,et al.  Constraint Databases , 2010, Springer Berlin Heidelberg.

[7]  Peter Z. Revesz,et al.  Introduction to Constraint Databases , 2002, Texts in Computer Science.

[8]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[9]  Jixian Zhang,et al.  An on-line potato-sack theorem , 1991, Discret. Comput. Geom..

[10]  Joseph R. Shoenfield,et al.  Mathematical logic , 1967 .

[11]  A. Dawar FINITE MODEL THEORY (Perspectives in Mathematical Logic) , 1997 .

[12]  M. Coste AN INTRODUCTION TO SEMIALGEBRAIC GEOMETRY , 2002 .

[13]  Christof Löding,et al.  A characterization of first-order topological properties of planar spatial data , 2006, J. ACM.

[14]  Gabriel M. Kuper,et al.  Constraint Query Languages , 1995, J. Comput. Syst. Sci..

[15]  Jianwen Su,et al.  First-order Definability over Constraint Databases , 1995, CP.

[16]  Alexei P. Stolboushkin,et al.  Linear vs. Order Contstrained Queries Over Rational Databases. , 1996, ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems.

[17]  Jan Paredaens,et al.  Towards a theory of spatial database queries (extended abstract) , 1994, PODS.

[18]  Michael Benedikt,et al.  Safe Constraint Queries , 2000, SIAM J. Comput..

[19]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

[20]  Jan Van den Bussche,et al.  Complete Geometric Query Languages , 1999, J. Comput. Syst. Sci..

[21]  Marc Giusti,et al.  A Gröbner Free Alternative for Polynomial System Solving , 2001, J. Complex..

[22]  B. F. Caviness,et al.  Quantifier Elimination and Cylindrical Algebraic Decomposition , 2004, Texts and Monographs in Symbolic Computation.

[23]  Th. Motzkin Beiträge zur Theorie der linearen Ungleichungen , 1936 .

[24]  M. Coste AN INTRODUCTION TO O-MINIMAL GEOMETRY , 2002 .

[25]  A Pettorossi Automata theory and formal languages , 2008 .

[26]  A. Seidenberg A NEW DECISION METHOD FOR ELEMENTARY ALGEBRA , 1954 .

[27]  Martin Grohe,et al.  On first-order topological queries , 2002, TOCL.

[28]  Michael Benedikt,et al.  Reachability and connectivity queries in constraint databases , 2003, J. Comput. Syst. Sci..

[29]  J. Risler,et al.  Real algebraic and semi-algebraic sets , 1990 .

[30]  Bart Kuijpers,et al.  On the decidability of termination of query evaluation in transitive-closure logics for polynomial constraint databases , 2005, Theor. Comput. Sci..

[31]  A. Tarski A Decision Method for Elementary Algebra and Geometry , 2023 .

[32]  Bart Kuijpers,et al.  Linear approximation of planar spatial databases using transitive-closure logic , 2000, PODS '00.

[33]  Jörg Flum,et al.  Finite model theory , 1995, Perspectives in Mathematical Logic.

[34]  Jianwen Su,et al.  Linear Constraint Query Languages: Expressive Power and Complexity , 1994, LCC.

[35]  L. van den Dries,et al.  Tame Topology and O-minimal Structures , 1998 .

[36]  Marc Gyssens,et al.  On Query Languages for Linear Queries Definable with Polynomial Constraints , 1996, CP.

[37]  M-F Roy,et al.  Géométrie algébrique réelle , 1987 .

[38]  A. Wilkie TAME TOPOLOGY AND O-MINIMAL STRUCTURES (London Mathematical Society Lecture Note Series 248) By L OU VAN DEN D RIES : 180 pp., £24.95 (US$39.95, LMS Members' price £18.70), ISBN 0 521 59838 9 (Cambridge University Press, 1998). , 2000 .

[39]  Limsoon Wong,et al.  Relational expressive power of constraint query languages , 1996, PODS.

[40]  Michael A. Taitslin,et al.  On Order-Generic Queries , 1996 .

[41]  D. V. Gucht,et al.  First-order queries on finite structures over the reals , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[42]  H. Jerome Keisler,et al.  Definability over Linear Constraints , 2000, CSL.

[43]  Joos Heintz,et al.  Description of the connected components of a semialgebraic set in single exponential time , 1994, Discret. Comput. Geom..

[44]  Michael Benedikt,et al.  On the structure of queries in constraint query languages , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[45]  Gabriel M. Kuper,et al.  Linear vs Polynomial Constraints in Database Query Languages , 1994, PPCP.