## On Transformations into Linear Database Logic Programs (1996)

### Cached

### Download Links

- [www.ionio.gr]
- [www.iit.nrcps.ariadne-t.gr]
- [softlab.ece.ntua.gr]
- DBLP

### Other Repositories/Bibliography

Venue: | Perspectives of Systems Informatics, 2nd International Andrei Ershov Memorial Conference, Akademgorodik |

Citations: | 6 - 5 self |

### BibTeX

@INPROCEEDINGS{Afrati96ontransformations,

author = {Foto Afrati and Manolis Gergatsoulis and Maria Katzouraki},

title = {On Transformations into Linear Database Logic Programs},

booktitle = {Perspectives of Systems Informatics, 2nd International Andrei Ershov Memorial Conference, Akademgorodik},

year = {1996},

pages = {433--444},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Abstract. We consider the problem of transformations of logic programs without function symbols (database logic programs) into a special subclass, namely linear logic programs. Linear logic programs are dened to be the programs whose rules have at most one intentional atom in their bodies. a) We investigate linearizability of several syntactically de ned subclasses of programs and present both positive and negative results (i.e. demonstrate programs that cannot be transformed into a linear program by any transformation technique), and b) We develop an algorithm which transforms any program in a speci c subclass namely the piecewise logic programs into a linear logic program.

### Citations

1913 |
Foundations of Logic Programming
- LLoyd
- 1987
(Show Context)
Citation Context ...pplication of this algorithm. Finally, in section 6, a conclusion is given. 2 Preliminaries In the following, we assume familiarity with the basic terminology of rst order logic and logic programming =-=[12]-=-. 2.1 Datalog programs Deductive database systems divide their information into two categories: The data which are represented by a predicate with constant arguments (all true tuples are stored in the... |

539 |
The complexity of relational query languages
- Vardi
- 1982
(Show Context)
Citation Context ...programs Because of their recursive nature, queries expressed in Datalog are harder to evaluate (from the point of view of parallel complexity): while rst-order queries are in deterministic log-space =-=[20]-=- (even in AC 0 ), Datalog programs are sometimes log-space complete for P: access(X) source(X): access(X) access(Y1)� access(Y2)� triple(Y1�Y2�X): The above program encodes the well-known path system ... |

227 | Unification revisited - Lassez, Maher, et al. - 1987 |

224 |
Unfold/fold transformation of logic programs
- Tamaki, Sato
- 1984
(Show Context)
Citation Context ... be linear i every rule in P has at most one intensional atom in its body. 2.2 Unfold/fold transformations Unfold/fold transformations[15, 17, 8, 9] for de nite clause programs were rst formulated in =-=[18]-=- so as to preserve the meaning of programs. The meaning M(P ) of a logic program P is de ned as: M(P )=fAjA is a ground atom which is a logical consequence of P g. M(P )isidentical to[12] the least He... |

204 |
An amateur’s introduction to recursive query processing strategies
- Bancilhon, Ramakrishnan
- 1986
(Show Context)
Citation Context ...rom the source nodes, then so is x. A large body of recent research has addressed the problems of nding e - cient evaluation methods and compile-time optimization techniques for Datalog programs (see =-=[5]-=- for a survey). These studies usually concentrate on syntactically restricted Datalog programs� two common approaches are the following: a) Restrict the width (number of arguments) of the IDB predicat... |

141 | Transformation of Logic Programs: Foundations and Techniques
- Pettorossi, Proietti
- 1994
(Show Context)
Citation Context ...h the predicate in its head, is included in its body. P is said to be linear i every rule in P has at most one intensional atom in its body. 2.2 Unfold/fold transformations Unfold/fold transformations=-=[15, 17, 8, 9]-=- for de nite clause programs were rst formulated in [18] so as to preserve the meaning of programs. The meaning M(P ) of a logic program P is de ned as: M(P )=fAjA is a ground atom which is a logical ... |

51 |
An observation on time-storage trade off
- Cook
- 1973
(Show Context)
Citation Context ...e sometimes log-space complete for P : access(X) / source(X): access(X) / access(Y 1 ); access(Y 2 ); triple(Y 1 ; Y 2 ; X): The above program encodes the well-known path system accessibility problem =-=[6]-=-: the EDB predicates source and triple represent, respectively, source nodes and accessibility conditions; triple(y 1 ; y 2 ; x) means that if y 1 ; y 2 are accessible from the source nodes, then so i... |

33 |
On Datalog vs. polynomial time
- Afrati, Cosmadakis, et al.
- 1991
(Show Context)
Citation Context ...owed). The results in part (a) above are presented in a uni ed way topoint out certain limits that program transformations cannot go beyond. They are proven after developing elaborate technical tools =-=[1, 3, 2]-=-. The results in part (b) are proven by presenting an algorithm that uses unfold/fold techniques in a coordinated form to arrive in a certain syntactically simpler program. On top on techniques used i... |

33 |
Parallel complexity of logical query programs
- Ullman, Gelder
- 1986
(Show Context)
Citation Context ... (number of arguments) of the IDB predicates. b) Impose a linearity condition on the rules (as, e.g., in [10, 13, 14]). It has been observed that linear Datalog programs can be evaluated in NC 2 (cf. =-=[7, 19]-=-). Moreover, all the Datalog programs currently known to be Pcomplete (see [7, 19, 4]) can be shown to require non-linear rules, because in each case there is a rst-order reduction from path system ac... |

24 |
Expressiveness of restricted recursive queries
- Afrati, Cosmodakis
- 1989
(Show Context)
Citation Context ...e non-linear programs by equivalent linear programs, because there are e cient algorithms for the computation of the latter which do not extend to the former. Linear programs have been widely studied =-=[1, 13, 4]-=- both as concerns their e ciency and the possibility of transformation of non-linear programs into linear. A program is linear if all the rules are linear, i.e., there is at most one intentional atom ... |

24 |
Data independent recursion in deductive databases
- Naughton
- 1986
(Show Context)
Citation Context ...e non-linear programs by equivalent linear programs, because there are e cient algorithms for the computation of the latter which do not extend to the former. Linear programs have been widely studied =-=[1, 13, 4]-=- both as concerns their e ciency and the possibility of transformation of non-linear programs into linear. A program is linear if all the rules are linear, i.e., there is at most one intentional atom ... |

24 |
The loop absorption and the generalization strategies for the development of logic programs and partial deduction. The
- Proietti, Pettorossi
- 1993
(Show Context)
Citation Context ...The results in part (b) are proven by presenting an algorithm that uses unfold/fold techniques in a coordinated form to arrive in a certain syntactically simpler program. On top on techniques used in =-=[16, 17]-=-, we had to develop some more technical tools to show our results. The results presented here are also interesting in view of the fact that they attack, the problem of program transformation from the ... |

21 |
A decidable class of bounded recursions
- Naughton, Sagiv
- 1987
(Show Context)
Citation Context ...lly restricted Datalog programs� two common approaches are the following: a) Restrict the width (number of arguments) of the IDB predicates. b) Impose a linearity condition on the rules (as, e.g., in =-=[10, 13, 14]-=-). It has been observed that linear Datalog programs can be evaluated in NC 2 (cf. [7, 19]). Moreover, all the Datalog programs currently known to be Pcomplete (see [7, 19, 4]) can be shown to require... |

19 | Unfold/fold transformations for definite clause programs
- Gergatsoulis, Katzouraki
- 1994
(Show Context)
Citation Context ...the predicate in its head, is included in its body. P is said to be linear iff every rule in P has at most one intensional atom in its body. 2.2 Unfold/fold transformations Unfold/fold transformations=-=[15, 17, 8, 9]-=- for definite clause programs were first formulated in [18] so as to preserve the meaning of programs. The meaning M(P ) of a logic program P is defined as: M(P ) = fAjA is a ground atom which is a lo... |

17 |
Parallel evaluation of recursive rule queries
- Cosmadakis, Kanellakis
- 1986
(Show Context)
Citation Context ... (number of arguments) of the IDB predicates. b) Impose a linearity condition on the rules (as, e.g., in [10, 13, 14]). It has been observed that linear Datalog programs can be evaluated in NC 2 (cf. =-=[7, 19]-=-). Moreover, all the Datalog programs currently known to be Pcomplete (see [7, 19, 4]) can be shown to require non-linear rules, because in each case there is a rst-order reduction from path system ac... |

17 |
The synthesis of eureka predicates for developing logic programs
- Proietti, Pettorossi
- 1990
(Show Context)
Citation Context ...The results in part (b) are proven by presenting an algorithm that uses unfold/fold techniques in a coordinated form to arrive in a certain syntactically simpler program. On top on techniques used in =-=[16, 17]-=-, we had to develop some more technical tools to show our results. The results presented here are also interesting in view of the fact that they attack, the problem of program transformation from the ... |

15 |
The parallel complexity of simple chain queries
- Afrati, Papadimitriou
- 1987
(Show Context)
Citation Context ...e non-linear programs by equivalent linear programs, because there are e cient algorithms for the computation of the latter which do not extend to the former. Linear programs have been widely studied =-=[1, 13, 4]-=- both as concerns their e ciency and the possibility of transformation of non-linear programs into linear. A program is linear if all the rules are linear, i.e., there is at most one intentional atom ... |

11 | A Time Bound on the Materialization of Some Recursively Defined Views 385 [Ioan] [Lewi] [Mink] [Naug] [Reit] [Sagi 1] [Sagi 2] [Ston] [Viei - Ioannidis - 1985 |

9 |
Uni cation revisited
- Lassez, Maher, et al.
- 1988
(Show Context)
Citation Context ...ause with a body atom that does not unify with the head of any clause in the program. A failing clause can be removed from the program. 4 The best choice is to use as I the most speci c generalization=-=[11]-=- ofID and IF.In [11], an algorithm to compute the most speci c generalization of a set of expressions is given. 8s3. Select the (possibly trivial) minimal upper portion MU of U so as each leaf clause ... |

6 |
Unfold/fold transformations for de nite clause programs
- Gergatsoulis, Katzouraki
- 1994
(Show Context)
Citation Context ...h the predicate in its head, is included in its body. P is said to be linear i every rule in P has at most one intensional atom in its body. 2.2 Unfold/fold transformations Unfold/fold transformations=-=[15, 17, 8, 9]-=- for de nite clause programs were rst formulated in [18] so as to preserve the meaning of programs. The meaning M(P ) of a logic program P is de ned as: M(P )=fAjA is a ground atom which is a logical ... |

2 |
An observation on time-storage trade o
- Cook
- 1974
(Show Context)
Citation Context ...log programs are sometimes log-space complete for P: access(X) source(X): access(X) access(Y1)� access(Y2)� triple(Y1�Y2�X): The above program encodes the well-known path system accessibility problem =-=[6]-=-: the EDB predicates source and triple represent, respectively, source nodes and accessibility conditions� triple(y1�y2�x) means that if y1�y2 are accessible from the source nodes, then so is x. A lar... |

2 |
A time bound on the materialization of some recursively de ned views
- Ioannidis
- 1985
(Show Context)
Citation Context ...lly restricted Datalog programs� two common approaches are the following: a) Restrict the width (number of arguments) of the IDB predicates. b) Impose a linearity condition on the rules (as, e.g., in =-=[10, 13, 14]-=-). It has been observed that linear Datalog programs can be evaluated in NC 2 (cf. [7, 19]). Moreover, all the Datalog programs currently known to be Pcomplete (see [7, 19, 4]) can be shown to require... |

1 |
Logic program transformations: Rules and application strategies
- Gergatsoulis
- 1994
(Show Context)
Citation Context ...h the predicate in its head, is included in its body. P is said to be linear i every rule in P has at most one intensional atom in its body. 2.2 Unfold/fold transformations Unfold/fold transformations=-=[15, 17, 8, 9]-=- for de nite clause programs were rst formulated in [18] so as to preserve the meaning of programs. The meaning M(P ) of a logic program P is de ned as: M(P )=fAjA is a ground atom which is a logical ... |