On compiling queries in recursive first-order databases
Journal of the ACM (JACM)
On the implementation of a simple class of logic queries for databases
PODS '86 Proceedings of the fifth ACM SIGACT-SIGMOD symposium on Principles of database systems
Naive evaluation of recursively defined relations
On knowledge base management systems: integrating artificial intelligence and d atabase technologies
Magic sets and other strange ways to implement logic programs (extended abstract)
PODS '86 Proceedings of the fifth ACM SIGACT-SIGMOD symposium on Principles of database systems
Parallel evaluation of recursive rule queries
PODS '86 Proceedings of the fifth ACM SIGACT-SIGMOD symposium on Principles of database systems
The generalized counting method for recursive logic queries
Proceedings on International conference on database theory
An amateur's introduction to recursive query processing strategies
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Traversal recursion: a practical approach to supporting recursive applications
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Evaluation of database recursive logic programs as recurrent function series
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Bounds on the propagation of selection into logic programs
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Decidability and expressiveness aspects of logic queries
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Query optimization by simulated annealing
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
A necessary condition for a doubly recursive rule to be equivalent to a linear recursive rule
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Programming in Prolog
Compiling separable recursions
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
Minimizing function-free recursive inference rules
Journal of the ACM (JACM)
Performance evaluation of data intensive logic programs
Foundations of deductive databases and logic programming
Proof-tree transformation theorems and their applications
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Linearising nonlinear recursions in polynomial time
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On compile-time query optimization in deductive databases by means of static filtering
ACM Transactions on Database Systems (TODS)
Argument reduction by factoring
VLDB '89 Proceedings of the 15th international conference on Very large data bases
Necessary and sufficient conditions to linearize doubly recursive programs in logic databases
ACM Transactions on Database Systems (TODS)
Commutativity and its role in the processing of linear recursion
Journal of Logic Programming
Optimizing existential datalog queries
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Equivalences Among Relational Expressions with the Union and Difference Operators
Journal of the ACM (JACM)
Contributions to the Theory of Logic Programming
Journal of the ACM (JACM)
A relational model of data for large shared data banks
Communications of the ACM
Automata, Languages, and Machines
Automata, Languages, and Machines
Universality of data retrieval languages
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Moving Selections into Linear Least Fixpoint Queries
IEEE Transactions on Knowledge and Data Engineering
Some Performance Results on Recursive Query Processing in Relational Database Systems
Proceedings of the Second International Conference on Data Engineering
Translation and Optimization of Logic Queries: The Algebraic Approach
VLDB '86 Proceedings of the 12th International Conference on Very Large Data Bases
On the Computation of the Transitive Closure of Relational Operators
VLDB '86 Proceedings of the 12th International Conference on Very Large Data Bases
Optimization of Systems of Algebraic Equations for Evaluating Datalog Queries
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Magic Functions: A Technique to Optimize Extended Datalog Recursive Programs
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Containment of conjunctive queries: beyond relations as sets
ACM Transactions on Database Systems (TODS)
Linearizing Some Recursive Logic Programs
IEEE Transactions on Knowledge and Data Engineering
A Graph-Based Framework for Multiparadigmatic Visual Access to Databases
IEEE Transactions on Knowledge and Data Engineering
Linearisability on datalog programs
Theoretical Computer Science
On Simplification of Database Integrity Constraints
Fundamenta Informaticae
Efficient integrity checking for databases with recursive views
ADBIS'05 Proceedings of the 9th East European conference on Advances in Databases and Information Systems
On Simplification of Database Integrity Constraints
Fundamenta Informaticae
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An algebraic framework for the study of recursion has been developed. For immediate linear recursion, a Horn clause is represented by a relational algebra operator. It is shown that the set of all such operators forms a closed semiring. In this formalism, query answering corresponds to solving a linear equation. For the first time, the query answer is able to be expressed in an explicit algebraic form within an algebraic structure. The manipulative power thus afforded has several implications on the implementation of recursive query processing algorithms. Several possible decompositions of a given operator are presented that improve the performance of the algorithms, as well as several transformations that give the ability to take into account any selections or projections that are present in a givin query. In addition, it is shown that mutual linear recursion can also be studied within a closed semiring, by using relation vectors and operator matrices. Regarding nonlinear recursion, it is first shown that Horn clauses always give rise to multilinear recursion, which can always be reduced to bilinear recursion. Bilinear recursion is then shown to form a nonassociative closed semiring. Finally, several sufficient and necessary-and-sufficient conditions for bilinear recursion to be equivalent to a linear one of a specific form are given. One of the sufficient conditions is derived by embedding to bilinear recursion in an algebra.