Interpretation of Stream Programs: Characterizing Type 2 Polynomial Time Complexity

Férée, Hugo; Hainry, Emmanuel; Hoyrup, Mathieu; Péchoux, Romain

doi:10.1007/978-3-642-17517-6_27

Cited by 8 publications

(7 citation statements)

References 15 publications

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“…Using an approach similar to the one presented in this paper, Férée et al [16] show that interpretations can be used on stream programs also to characterize type 2 polynomial time functions. In particular, they extend interpretations in order to use second order polynomials to characterize the set of functions computable in polynomial time by Oracle Turing Machines and by their unitary version.…”

Section: Related Workmentioning

confidence: 99%

On bounding space usage of streams using interpretation analysis

Gaboardi

Péchoux

2015

Science of Computer Programming

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Interpretation methods are important tools in implicit computational complexity. They have been proved particularly useful to statically analyze and to limit the complexity of programs. However, most of these studies have been so far applied in the context of term rewriting systems over finite data.In this paper, we show how interpretations can also be used to study properties of lazy first-order functional programs over streams. In particular, we provide some interpretation criteria useful to ensure two kinds of stream properties: space upper bounds and input/output upper bounds. Our space upper bounds criteria ensures global and local upper bounds on the size of each output stream element expressed in terms of the maximal size of the input stream elements. The input/output upper bounds criteria consider instead the relations between the number of elements read from the input stream and the number of elements produced on the output stream.This contribution can be seen as a first step in the development of a methodology aiming at using interpretation properties to ensure space safety properties of programs working on streams.

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Section: Related Workmentioning

confidence: 99%

On bounding space usage of streams using interpretation analysis

Gaboardi

Péchoux

2015

Science of Computer Programming

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“…Using an approach based on quasi-interpretation, in [12,13] we have studied space upper bounds properties and input-output properties of programs working on streams. Using a similar approach Férée et al [10] showed that interpretations can be used on stream programs also to characterize type 2 polynomial time functions by providing a characterization of the class of the Basic Feasible Functionals of Cook and Urquhart [9].…”

Section: Related Workmentioning

confidence: 99%

Algebras and coalgebras in the light affine Lambda calculus

GaboardiMarco

PéchouxRomain

2015

SIGPLAN Not.

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Algebra and coalgebra are widely used to model data types in functional programming languages and proof assistants. Their use permits to better structure the computations and also to enhance the expressivity of a language or of a proof system. Interestingly, parametric polymorphismà la System F provides a way to encode algebras and coalgebras in strongly normalizing languages without loosing the good logical properties of the calculus. Even if these encodings are sometimes unsatisfying because they provide only limited forms of algebras and coalgebras, they give insights on the expressivity of System F in terms of functions that we can program in it. With the goal of contributing to a better understanding of the expressivity of Implicit Computational Complexity systems, we study the problem of defining algebras and coalgebras in the Light Affine Lambda Calculus, a system characterizing the complexity class FPTIME. In this system, the principle of stratification limits the ways we can use parametric polymorphism, and in general the way we can write our programs. We show here that while stratification poses some issues to the standard System F encodings, it still permits to encode some weak form of algebra and coalgebra. Using the algebra encoding one can define in the Light Affine Lambda Calculus the traditional inductive types. Unfortunately, the corresponding coalgebra encoding permits only a very limited form of coinductive data types. To extend this class we study an extension of the Light Affine Lambda Calculus by distributive laws for the modality §. This extension has been discussed but not studied before.

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Section: Related Workmentioning

confidence: 99%