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Page 7669 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
Yasuhara (Princeton, NJ) 2001k:03064 03C10 03B25 12DI15 68P15 68Q25 68W30 Basu, Saugata (1-MI; Ann Arbor, MI) New results on quantifier elimination over real closed fields and applications to constraint  ...  “Using the uniform quantifier elimination algorithm, we give an algorithm for solving a problem arising in the field of constraint databases with real polynomial constraints, that is, for converting a  ... 

The evaluation of geometric queries: constraint databases and quantifier elimination [article]

Marc Giusti, Joos Heintz, Bart Kuijpers
2011 arXiv   pre-print
We model the algorithmic task of geometric elimination (e.g., quantifier elimination in the elementary field theories of real and complex numbers) by means of certain constraint database queries, called  ...  Although this paper is of theoretical nature, its aim is to explore the possibilities and (complexity-)limits of computer implemented query evaluation algorithms for Constraint Databases, based on the  ...  When we consider constraint databases over the real numbers, a generalized relation is finitely represented by a Boolean combination of polynomial equalities and inequalities over the reals.  ... 
arXiv:1110.2196v2 fatcat:syvu4bcz5beo5axshzlnfdkrb4

Constraint Databases, Data Structures and Efficient Query Evaluation [chapter]

Joos Heintz, Bart Kuijpers
2004 Lecture Notes in Computer Science  
We emphasize the importance of data structures and their effect on the complexity of quantifier-elimination.  ...  Constraint databases that can be described by boolean combinations of polynomial inequalities over the reals have received ample research attention.  ...  for Constraint Database Systems" of the FWO-Vlaanderen and SECyT, Argentina.  ... 
doi:10.1007/978-3-540-25954-1_1 fatcat:3j4o74pdkvdi5bwl5sfyctiq5i

Queries with arithmetical constraints

Stéphane Grumbach, Jianwen Su
1997 Theoretical Computer Science  
Finally, we developed reduction techniques for queries over constraint databases, that allow us to draw conclusions with respect to their undefinability in various constraint query languages.  ...  We prove in particular that linear queries can be evaluated in AC0 over finite integer databases, and in NC' over linear constraint databases. This improves previously known bounds.  ...  These constraints are based on decidable theories that admit elimination of quantifiers.  ... 
doi:10.1016/s0304-3975(96)00194-6 fatcat:2l24uv556reahd6xv2u57wxgqu

Datalog with Constraints: A Foundation for Trust Management Languages [chapter]

Ninghui Li, John C. Mitchell
2002 Lecture Notes in Computer Science  
Although constraint Datalog has been studied in the context of constraint databases, TM applications involve different kinds of constraint domains and have different computational complexity requirements  ...  We also present a concrete declarative TM language, RT C 1 , based on constraint Datalog, and use constraint Datalog to analyze another TM system, KeyNote, which turns out to be less expressive than RT  ...  The domain of polynomial constraints over real numbers admits quantifier elimination, but the complexity is very high.  ... 
doi:10.1007/3-540-36388-2_6 fatcat:cpupygxrvza4hhdyy27h7xenoq

Quantifier-Elimination for the First-Order Theory of Boolean Algebras with Linear Cardinality Constraints [chapter]

Peter Revesz
2004 Lecture Notes in Computer Science  
Since relational calculus is closely tied with practical query languages like SQL, it has captured the most attention in the database area. quantifier elimination for real closed fields [2, 3, 12, 13,  ...  We also explain the connection of this new logical result with the evaluation of relational calculus queries on constraint databases that contain Boolean linear cardinality constraints.  ...  Conclusions and Future Work Quantifier elimination from Boolean linear cardinality constraint formulas by reduction to quantifier elimination in Presburger arithmetic is a new approach.  ... 
doi:10.1007/978-3-540-30204-9_1 fatcat:4jaji3a2pjcfbit3suhp3jq3jm

An incremental algorithm for DLO quantifier elimination via constraint propagation

Matti Nykänen
2004 Artificial Intelligence  
The first-order logical theory of dense linear order has long been known to admit quantifier elimination.  ...  The result is computed incrementally using functional programming techniques. This approach may be of interest in implementing query languages for constraint databases.  ...  Indeed, constraint databases are an eminent application area for a quantifier elimination algorithm over real closed fields [3] , since constraint databases require arithmetic on real numbers rather than  ... 
doi:10.1016/j.artint.2004.05.011 fatcat:gmlrsqo4arfpdbyo3lymiq32iy

Real Algebraic Geometry and Constraint Databases [chapter]

Floris Geerts, Bart Kuijpers
2007 Handbook of Spatial Logics  
The constraint database model can be seen as a generalization of the classical relational database model that was introduced by Codd in the 1970s to deal with the management of alpha-numerical data, typically  ...  A relational database is usually modeled following a database schema. A schema contains information on the relation names and on the names of the attributes appearing in relation.  ...  However, since the triviality theorem does not hold in this case, one first needs to develop an alternative decomposition theorem (see (?) for details).  ... 
doi:10.1007/978-1-4020-5587-4_13 fatcat:5oemzcnwe5egnkkrjxquwsl5ve

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Manolis Koubarakis
2012 Applied intelligence (Boston)  
To make our claim more persuasive, we survey previous works on querying temporal constraint networks and show that they can be viewed as an instance of the scheme of indefinite constraint databases.  ...  The extra representational power allows us to express temporal knowledge and queries that have been impossible to express before.  ...  I would like to thank Spiros Skiadopoulos for his contributions on related work, and Paolo Terenziani for detailed comments on a previous version of this paper.  ... 
doi:10.1023/a:1020043517392 fatcat:f7xhmzdsbfgmvp3tgbhhzsfw4u

Constraint Query Languages [chapter]

Floris Geerts
2017 Encyclopedia of Database Systems  
Definition A constraint query language is a query language for constraint databases.  ...  In order to obtain an O-constraint relation, one needs perform quantifier-elimination.  ...  Denote the resulting formula by plug(', D); and (ii) eliminate the quantifiers in plug(', D).  ... 
doi:10.1007/978-1-4899-7993-3_1240-2 fatcat:se4frihzr5g4zkbjljg6ldhqde

First‐Order Languages Expressing Constructible Spatial Database Queries

Bart Kuijpers, Gabriel Kuper, Jan Paredaens, Luc Vandeurzen
2007 SIAM journal on computing (Print)  
The aim of this paper is to identify a class of two-dimensional constraint databases and a query language within the constraint model that go beyond the linear model and allow the expression of queries  ...  The research presented in this paper is situated in the framework of constraint databases introduced by Kanellakis, Kuper, and Revesz in their seminal paper of 1990, specifically, the language with real  ...  Due to this complexity it seems to be infeasible for real spatial database applications to rely on quantifier elimination (we discuss this further below).  ... 
doi:10.1137/s0097539702407199 fatcat:bxtci6no5zamjgirhcne7yshwm

On the Fixpoint Theory of Equality and Its Applications [chapter]

Andrzej Szałas, Jerzy Tyszkiewicz
2006 Lecture Notes in Computer Science  
The motivation behind considering this theory is that second-order quantifier elimination techniques based on a theorem given in [16] , when successful, often result in such formulas.  ...  This opens many applications, including automated theorem proving, static verification of integrity constraints in databases as well as reasoning with weakest sufficient and strongest necessary conditions  ...  Below we propose another method, which seems to be new in the field. It is not based on any particular proof system.  ... 
doi:10.1007/11828563_26 fatcat:4az2szfmdvguxif2vkc5fu6l6e

Finitely Representable Databases

Stéphane Grumbach, Jianwen Su
1997 Journal of computer and system sciences (Print)  
We study infinite but finitely representable databases based on constraints, motivated by new database applications such as those involving spatio-temporal information.  ...  As a case study, we focus on queries over dense order constraint databases.  ...  ACKNOWLEDGMENTS The authors thank Victor Vianu and the referees for helpful comments.  ... 
doi:10.1006/jcss.1997.1524 fatcat:wnufsjymt5hhdemdf3ersmn4xe

Mathematics mechanization and applications after thirty years

Wenjun Wu, Xiaoshan Gao
2007 Frontiers of Computer Science in China  
This paper gives a brief review of the major advances in the field over the past thirty years.  ...  Finally, applications in computer-aided geometric design, computer vision, intelligent computeraided design, and robotics are surveyed.  ...  Historically, Tarski's landmark work on quantifier elimination over the field of real numbers provides a complete method to prove all elementary theorems from Euclidean geometry.  ... 
doi:10.1007/s11704-007-0001-8 fatcat:7iia43igzrckfnzchtg5jll5eq

The Expressivity of Constraint Query Languages with Boolean Algebra Linear Cardinality Constraints [chapter]

Peter Revesz
2005 Lecture Notes in Computer Science  
Constraint query languages with Boolean algebra linear cardinality constraints were introduced recently and shown to be evaluable using a quantifier elimination method in [22] .  ...  Finally, we also show a new results for F O + LIN EAR by expressing in it the problem of finding the time when two linearly moving point objects are closest to each other.  ...  Tarski [25] gave the first decision procedure and quantifier elimination algorithm for the real closed fields, but more efficient algorithms include [2, 5, 9, 19] .  ... 
doi:10.1007/11547686_13 fatcat:ocvjusxfejgwtfbhz3dc2t2obq
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