Program transformation by solving recurrences

Luca, Beatrice; Andrei, Ștefan; Anderson, Hugh; Khoo, Siau‐Cheng

doi:10.1145/1111542.1111563

Cited by 4 publications

(5 citation statements)

References 17 publications

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“…There are a number of cost analyses available which are based on building CRs and which can handle a range of programming languages, including functional [18,36,40,47,49,53,54], logic [26,42], and imperative [6]. Such CRs must ensure that, for any valid input integer tuple, a value which is guaranteed to be an upper bound of the execution cost of the program for any input data in the (usually infinite) set of values which are consistent with the input sizes.…”

Section: Related Workmentioning

confidence: 99%

“…One alternative consists in implementing restricted recurrence solvers within the analyzer based on standard mathematical techniques, as done in [26,54]. The other alternative, motivated by the availability of powerful computer algebra systems (CASs for short) such as Mathematica ® , MAXIMA, MAPLE, etc., consists in connecting the analyzer with an external solver, as proposed in [6,18,40,49,53].…”

Section: Related Workmentioning

confidence: 99%

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Closed-Form Upper Bounds in Static Cost Analysis

et al. 2010

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The classical approach to automatic cost analysis consists of two phases. Given a program and some measure of cost, the analysis first produces cost relations (CRs), i.e., recursive equations which capture the cost of the program in terms of the size of its input data. Second, CRs are converted 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 been comparatively less studied. This article presents, to our knowledge, the first practical framework for the generation of closed-form upper bounds for CRs which (1) is fully automatic, (2) can handle the distinctive features of CRs, originating from cost analysis of realistic programming languages, (3) is not restricted to simple complexity classes, and (4) produces reasonably accurate solutions. A key idea in our approach is to view CRs as programs, which allows applying semantic-based static analyses and transformations to bound them, namely our method is based on the inference of ranking functions and loop invariants and on the use of partial evaluation.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Closed-Form Upper Bounds in Static Cost Analysis

et al. 2010

View full text Add to dashboard Cite

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“…[57,22]. The other alternative, motivated by the availability of powerful computer algebra systems (CASs for short) such as Mathematica, MAXIMA, MAPLE, etc., consists in connecting the analyzer with an external solver, as proposed in [56,47,14,6,38].…”

Section: Systems For Computing Closed-form Upper-boundsmentioning

confidence: 99%

Resource Usage Analysis and Its Application to Resource Certification

Albert

Arenas

Genaim

et al. 2009

Foundations of Security Analysis and Design V

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Abstract. Resource usage is one of the most important characteristics of programs. Automatically generated information about resource usage can be used in multiple ways, both during program development and deployment. In this paper we discuss and present examples on how such information is obtained in COSTA, a state of the art static analysis system. COSTA obtains safe symbolic upper bounds on the resource usage of a large class of general-purpose programs written in a mainstream programming language such as Java (bytecode). We also discuss the application of resource-usage information for code certification, whereby code not guaranteed to run within certain user-specified bounds is rejected.

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“…Multiple analysis have been developed for different paradigms including for functional [Benzinger 2004;Hoffmann et al 2011;Le Metayer 1988;Luca et al 2006;Rosendahl 1989;Sands 1995;Wadler 1988;Wegbreit 1975], logic [Debray and Lin 1993;Navas et al 2007], and imperative [Adachi et al 1979;Albert et al 2012] programming languages. Importantly, the resulting CRs are a common target of cost analyzers, that is, they abstract away the particular features of the original programming language and (at least conceptually) have the same form.…”

Section: Introductionmentioning

confidence: 99%

On the Inference of Resource Usage Upper and Lower Bounds

Albert

Genaim

Masud

2013

ACM Trans. Comput. Logic

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Cost analysis aims at determining the amount of resources required to run a program in terms of its input data sizes. The most challenging step is to infer the cost of executing the loops in the program. This requires bounding the number of iterations of each loop and finding tight bounds for the cost of each of its iterations. This article presents a novel approach to infer upper and lower bounds from cost relations. These relations are an extended form of standard recurrence equations that can be nondeterministic, contain inexact size constraints and have multiple arguments that increase and/or decrease. We propose novel techniques to automatically transform cost relations into worst-case and best-case deterministic one-argument recurrence relations. The solution of each recursive relation provides a precise upper-bound and lower-bound for executing a corresponding loop in the program. Importantly, since the approach is developed at the level of the cost equations, our techniques are programming language independent.

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Program transformation by solving recurrences

Cited by 4 publications

References 17 publications

Closed-Form Upper Bounds in Static Cost Analysis

Closed-Form Upper Bounds in Static Cost Analysis

Resource Usage Analysis and Its Application to Resource Certification

On the Inference of Resource Usage Upper and Lower Bounds

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