## A New Meta-Complexity Theorem for Bottom-up Logic Programs (2001)

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Venue: | In Proceedings of the International Joint Conference on Automated Reasoning, Lecture Notes in Computer Science |

Citations: | 30 - 2 self |

### BibTeX

@INPROCEEDINGS{Ganzinger01anew,

author = {Harald Ganzinger and David Mcallester},

title = {A New Meta-Complexity Theorem for Bottom-up Logic Programs},

booktitle = {In Proceedings of the International Joint Conference on Automated Reasoning, Lecture Notes in Computer Science},

year = {2001},

pages = {514--528},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Nontrivial meta-complexity theorems, proved once for a programming

### Citations

892 | A Theory of Objects
- Abadi, Cardelli
- 1996
(Show Context)
Citation Context ...roportional to the number of input clauses in D. 6 Henglein's Quadratic Typability Algorithm Following the exposition by [10], the typability problem in a variant of the AbadiCardelli object calculus [1] considered by [8] can be taken to consist of a given set of assertions of the form and accepts(; l) and notaccepts(; l), where and are type names and l is a message name. The instance is ... |

311 |
Linear-time algorithms for testing the satisfiability of propositional Horn formulæ
- Dowling, Gallier
- 1984
(Show Context)
Citation Context ...n the congruence closure module. We start with the following linear time module for ground Horn clauses without equality. The module may be viewed as a high-level implementation of 8sthe algorithm in =-=[4]-=-. The main idea in this set of rules is that atoms appearing in the antecedent of clauses are first detached from their clauses. This has the effect that even if an atom has many occurrences in antece... |

199 |
H.: Rewrite-Based Equational Theorem Proving with Selection and Simplification
- Bachmair, Ganzinger
- 1994
(Show Context)
Citation Context ...y theorem requires that deletion be permanent | once an assertion is deleted further attempts to reassert it have no eect. (If deletion is based on a notion of redundancy such as the one proposed in [=-=2]-=-, once an assertion has become redundant it remains so for the remainder of the computation.) To see the problem with deletion consider the simple pair of rules [P ] ! Q and [Q] ! P . If deletion is c... |

106 |
Variations on the common subexpression problem
- Downey, Sethi, et al.
- 1980
(Show Context)
Citation Context ...og n) algorithm for congruence closure. The rules are related to rules given in [3] which view congruence closure as a form of ground completion. The ternary atoms h ; i ) represent the signatures in =-=[5-=-], or the denitions in [3]. Note that, by contrast to [3], we do not introduce new constants to denote the subterms of the input equations. The terms on the right side in ) play the role of these cons... |

65 | On the complexity analysis of static analyses
- McAllester
- 2002
(Show Context)
Citation Context ...eatly facilitating their analysis. 1 Introduction McAllester has recently shown that the running time of a bottom-up logic program can be bounded by the number of \prexsrings" of its inference ru=-=les [-=-10]. A prexsring of a rule is a derivable instantiation of a prex of the antecedents of that rule. This single nontrivial meta-complexity theorem simplies the presentation and complexity analysis of a... |

62 | Automatic recognition of tractability in inference relations
- McAllester
- 1993
(Show Context)
Citation Context ...this work should be extended. Theorem 4 should be generalized to cases of input clauses with variables. However, already in the given form it is useful for local (equational) theories in the sense of =-=[7, 9, 6]-=-. The relation between deletions and redundancy elimination, with redundancy in the sense of [2] as entailment from smaller atoms, should be explored. For instance, the rule (I9) deletes push(s; t) if... |

36 |
Linear-time algorithms for testing the satis of propositional horn formulae
- Dowling, Gallier
- 1984
(Show Context)
Citation Context ... in the congruence closure module. We start with the following linear time module for ground Horn clauses without equality. The module may be viewed as a high-level implementation of the algorithm in =-=[4-=-]. The main idea in this set of rules is that atoms appearing in the antecedent of clauses aresrst detached from their clauses. This has the eect that even if an atom has many occurrences in anteceden... |

28 | New results on local inference relations
- Givan, McAllester
- 1992
(Show Context)
Citation Context ...this work should be extended. Theorem 4 should be generalized to cases of input clauses with variables. However, already in the given form it is useful for local (equational) theories in the sense of =-=[7, 9, 6]-=-. The relation between deletions and redundancy elimination, with redundancy in the sense of [2] as entailment from smaller atoms, should be explored. For instance, the rule (I9) deletes push(s; t) if... |

22 | Relating semantic and proof-theoretic concepts for polynomial time decidability of uniform word problems
- Ganzinger
- 2001
(Show Context)
Citation Context ...this work should be extended. Theorem 4 should be generalized to cases of input clauses with variables. However, already in the given form it is useful for local (equational) theories in the sense of =-=[7, 9, 6]-=-. The relation between deletions and redundancy elimination, with redundancy in the sense of [2] as entailment from smaller atoms, should be explored. For instance, the rule (I9) deletes push(s; t) if... |

8 | Breaking through the n � barrier: Faster object type inference
- Henglein
- 1997
(Show Context)
Citation Context ... number of input clauses in D. 6 Henglein's Quadratic Typability Algorithm Following the exposition by [10], the typability problem in a variant of the AbadiCardelli object calculus [1] considered by [8] can be taken to consist of a given set of assertions of the form and accepts(; l) and notaccepts(; l), where and are type names and l is a message name. The instance is acceptable (solvab... |

5 | Breaking through the n 3 barrier: Faster object type inference
- Henglein
- 1997
(Show Context)
Citation Context ... number of input clauses in D. 6 Henglein’s Quadratic Typability Algorithm Following the exposition by [10], the typability problem in a variant of the AbadiCardelli object calculus [1] considered by =-=[8]-=- can be taken to consist of a given set of assertions of the form σ ≤ τ and accepts(σ, l) and notaccepts(σ, l), where σ and τ are type names and l is a message name. The instance is acceptable (solvab... |

2 |
Bachmair and Ashish Tiwari. Abstract congruence closure and specializations
- Leo
- 2000
(Show Context)
Citation Context ...priority lower than the rules (C4){(C7) that use the output predicate f ! ! of U ). Combined with U , they give an O(n log n) algorithm for congruence closure. The rules are related to rules given in =-=[3-=-] which view congruence closure as a form of ground completion. The ternary atoms h ; i ) represent the signatures in [5], or the denitions in [3]. Note that, by contrast to [3], we do not introduce n... |