Resource Analysis by Sup-interpretation

Marion, Jean-Yves; Péchoux, Romain

doi:10.1007/11737414_12

Cited by 18 publications

(20 citation statements)

References 18 publications

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“…We compensate for the loss of well-foundedness over real numbers by putting restriction on the considered quasi-orderings. Polynomial assignments are also related to quasi-interpretations (Bonfante et al 2007) and sup-interpretations (Marion and Péchoux 2006). These two notions provide upper bounds on the size of the values computed by a function symbol.…”

Section: Introductionmentioning

confidence: 97%

“…The third one considers imperative programming languages in (Niggl and Wunderlich 2006;Kristiansen and Jones 2005) and complexity analysis of Java (Albert et al a,b). The fourth approach is the one on which we focus in this paper which considers polynomial assignments, quasi-interpretations (Bonfante et al 2007) and sup-interpretations (Marion and Péchoux 2006). It is related to polynomial interpretations (Lankford 1979).…”

Section: Introductionmentioning

confidence: 98%

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Characterizations of polynomial complexity classes with a better intensionality

Marion

Péchoux

2008

Proceedings of the 10th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming

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In this paper, we study characterizations of polynomial complexity classes using first order functional programs and we try to improve their intensionality, that is the number of natural algorithms captured. We use polynomial assignments over the reals. The polynomial assignments used are inspired by the notions of quasiinterpretation and sup-interpretation, and are decidable when considering polynomials of bounded degree ranging over real numbers. Contrarily to quasi-interpretations, the considered assignments are not required to have the subterm property. Consequently, they capture a strictly larger number of natural algorithms (including quotient, gcd, duplicate elimination from a list) than previous characterizations using quasi-interpretations.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

Characterizations of polynomial complexity classes with a better intensionality

Marion

Péchoux

2008

Proceedings of the 10th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming

Self Cite

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“…Intuitively, the supinterpretation is a special program interpretation which bounds from above the output size of the function denoted by the program, as demonstrated in the following lemma: Lemma 1 ( [27]). Given a sup-interpretation θ and an expression e defined over dom(θ), if e ∈ Values then we have | e | ≤ θ * ( e ) ≤ θ * (e) Example 3.…”

Section: Sup-interpretationsmentioning

confidence: 99%

A Characterization of NC k by First Order Functional Programs

Marion

Péchoux

Lecture Notes in Computer Science

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Abstract. This paper is part of a research on static analysis in order to predict program resources and belongs to the implicit computational complexity line of research. It presents intrinsic characterizations of the classes of functions, which are computable in NC k , that is by a uniform, poly-logarithmic depth and polynomial size family of circuits, using first order functional programs. Our characterizations are new in terms of first order functional programming language and extend the characterization of NC 1 in [9]. These characterizations are obtained using a complexity measure, the sup-interpretation, which gives upper bounds on the size of computed values and captures a lot of program schemas.

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“…al. [19,8] use a kind of polynomial ranking functions, but the approach is limited to polynomial bounds and can only handle a rather restricted form of CRs.…”

Section: Introductionmentioning

confidence: 99%

Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis

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Abstract. The classical approach to automatic cost analysis consists of two phases. Given a program and some measure of cost, we first produce recurrence relations (RRs) which capture the cost of our program in terms of the size of its input data. Second, we convert such RRs into closed form (i.e., without recurrences). Whereas the first phase has received considerable attention, with a number of cost analyses available for a variety of programming languages, the second phase has received comparatively little attention. In this paper we first study the features of RRs generated by automatic cost analysis and discuss why existing computer algebra systems are not appropriate for automatically obtaining closed form solutions nor upper bounds of them. Then we present, to our knowledge, the first practical framework for the fully automatic generation of reasonably accurate upper bounds of RRs originating from cost analysis of a wide range of programs. It is based on the inference of ranking functions and loop invariants and on partial evaluation.

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Resource Analysis by Sup-interpretation

Cited by 18 publications

References 18 publications

Characterizations of polynomial complexity classes with a better intensionality

Characterizations of polynomial complexity classes with a better intensionality

A Characterization of NC k by First Order Functional Programs

Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis

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