Stratified functional programs and computational complexity

Leivant, Daniel

doi:10.1145/158511.158659

Cited by 66 publications

(50 citation statements)

References 10 publications

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“…Indexing base types is needed to define ramification conditions as in [20]; A n , in particular, is not a cartesian product. The notation A n ⊸ B is defined by induction on n as follows:…”

Section: Figure 1 Type Assignment Rulesmentioning

confidence: 99%

“…The resulting subsystems are then shown to correspond to complexity classes by way of a number of different, heterogeneous techniques. Many kinds of constraints have been shown to be useful in this context; this includes ramification [3,20,22], linear types [17,4,21,8] and restricted exponentials [14,19]. However, the situation is far from being satisfactory.…”

Section: Introductionmentioning

confidence: 99%

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The geometry of linear higher-order recursion

Lago

2009

ACM Trans. Comput. Logic

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“…Indexing base types is needed to define ramification conditions as in [20]; A n , in particular, is not a cartesian product. The notation A n ⊸ B is defined by induction on n as follows:…”

Section: Figure 1 Type Assignment Rulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The geometry of linear higher-order recursion

Lago

2009

ACM Trans. Comput. Logic

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“…When some simple syntactic restrictions are applied to the list primitive recursive functions, these functions precisely characterize the polynomial time space [Bellantoni and Cook 1992;Leivant 1993].…”

Section: Advanced List Operationsmentioning

confidence: 99%

Optimizing object queries using an effective calculus

Fegaras

Maier

2000

ACM Trans. Database Syst.

110

104

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Object-oriented databases (OODBs) provide powerful data abstractions and modeling facilities, but they generally lack a suitable framework for query processing and optimization. The development of an effective query optimizer is one of the key factors for OODB systems to successfully compete with relational systems, as well as to meet the performance requirements of many nontraditional applications. We propose an effective framework with a solid theoretical basis for optimizing OODB query languages. Our calculus, called the monoid comprehension calculus, captures most features of ODMG OQL, and is a good basis for expressing various optimization algorithms concisely. This article concentrates on query unnesting (also known as query decorrelation), an optimization that, even though it improves performance considerably, is not treated properly (if at all) by most OODB systems. Our framework generalizes many unnesting techniques proposed recently in the literature, and is capable of removing any form of query nesting using a very simple and efficient algorithm. The simplicity of our method is due to the use of the monoid comprehension calculus as an intermediate form for OODB queries. The monoid comprehension calculus treats operations over multiple collection types, aggregates, and quantifiers in a similar way, resulting in a uniform method of unnesting queries, regardless of their type of nesting.

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“…After two decades from the pioneering works that started it [3,12,13], implicit computational complexity is now an active research area at the intersection of mathematical logic and computer science. Its aim is the study of machine-free characterizations of complexity classes.…”

Section: Introductionmentioning

confidence: 99%

Bounded Linear Logic, Revisited

Lago¹,

Hofmann²

2010

Log.Meth.Comput.Sci.

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Abstract. We present QBAL, an extension of Girard, Scedrov and Scott's bounded linear logic. The main novelty of the system is the possibility of quantifying over resource variables. This generalization makes bounded linear logic considerably more flexible, while preserving soundness and completeness for polynomial time. In particular, we provide compositional embeddings of Leivant's RRW and Hofmann's LFPL into QBAL.

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Stratified functional programs and computational complexity

Cited by 66 publications

References 10 publications

The geometry of linear higher-order recursion

The geometry of linear higher-order recursion

Optimizing object queries using an effective calculus

Bounded Linear Logic, Revisited

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