A theoretical study on the time analysis of programs

Adachi, Akeo; Kasai, Takeshi; Moriya, Etsuro

doi:10.1007/3-540-09526-8_16

Cited by 7 publications

(10 citation statements)

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“…While these upper bounds are tight for the class of programs as a whole, many programs of the class have a lower complexity, so we can try to analyze a given program more precisely. Works of this kind include [11,1,14,18,10]. With a single exception, these works proposed syntactic criteria, or analysis algorithms, that are sufficient for ensuring that the program lies in a desired class (say, polynomial-time programs), but are not both necessary and sufficient: thus, they do not address the decidability question (the exception is [14] which has a decidability result for a "core" language).…”

Section: Related Workmentioning

confidence: 99%

On the Edge of Decidability in Complexity Analysis of Loop Programs

Ben-Amram

Kristiansen

2012

Int. J. Found. Comput. Sci.

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We investigate the decidability of the feasibility problem for imperative programs with bounded loops. A program is called feasible if all values it computes are polynomially bounded in terms of the input. The feasibility problem is representative of a group of related properties, like that of polynomial time complexity. It is well known that such properties are undecidable for a Turing-complete programming language. They may be decidable, however, for languages that are not Turing-complete. But if these languages are expressive enough, they do pose a challenge for analysis. We are interested in tracing the edge of decidability for the feasibility problem and similar problems.In previous work, we proved that such problems are decidable for a language where loops are bounded but indefinite (that is, the loops may exit before completing the given iteration count). In this paper, we consider definite loops. A second language feature that we vary, is the kind of assignment statements. With ordinary assignment, we prove undecidability of a very tiny language fragment. We also prove undecidability with lossy assignment (that is, assignments where the modified variable may receive any value bounded by the given expression, even zero). But we prove decidability with max assignments (that is, assignments where the modified variable never decreases its value).

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Section: Related Workmentioning

confidence: 99%

On the Edge of Decidability in Complexity Analysis of Loop Programs

Ben-Amram

Kristiansen

2012

Int. J. Found. Comput. Sci.

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“…The name "step-counting version" is taken from [Adachi, Kasai & Moriya 1979 [Wadler 1988] with reference to [Métayer 1988], a time-complexity. The name complexity function is in both references used for the time bound function composed with the size measure.…”

Section: Definitionsmentioning

confidence: 99%

“…The paper describes a performance compiler to analyse a simple procedureless imperative language and it also contains results on the analysis of FP programs. [Adachi, Kasai & Moriya 1979] develops an algorithm to construct time bound programs for a class of imperative programs called simple loop programs.…”

Section: Related Workmentioning

confidence: 99%

Automatic complexity analysis

Rosendahl

1989

Proceedings of the Fourth International Conference on Functional Programming Languages and Computer Architecture - FPCA '89

132

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One way to analyse programs is to to derive expressions for their computational behaviour. A time bound function (or worst-case complexity) gives an upper bound for the computation time as a function of the size of input. We describe a system to derive such time bounds automatically using abstract interpretation. The semantics-based setting makes it possible to prove the correctness of the time bound function. The system can analyse programs in a first-order subset of Lisp and we show how the system also can be used to analyse programs in other languages.

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“…Also, Cousot and Cousot sketch an approach to performance analysis already in their seminal 1977 paper on abstract interpretation [10]. Since then, a good number of cost analysis frameworks for a wide variety of programming languages have been devised, including for functional [22,16,18,21,19,8], logic [13,17], and imperative [1,2] programming languages. An important observation of this paper is that the result of cost analysis in the different languages and programming paradigms can often be uniformly expressed as Cost Relation Systems (CRSs for short).…”

Section: Introductionmentioning

confidence: 99%

Cost Relation Systems: A Language-Independent Target Language for Cost Analysis

Albert

Arenas

Genaim

et al. 2009

Electronic Notes in Theoretical Computer Science

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Cost analysis aims at obtaining information about the execution cost of programs. This paper studies cost relation systems (CRSs): the sets of recursive equations used in cost analysis in order to capture the execution cost of programs in terms of the size of their input arguments. We investigate the notion of CRS from a general perspective which is independent of the particular cost analysis framework. Our main contributions are: we provide a formal definition of execution cost and of CRS which is not tied to a particular programming language; we present the notion of sound CRS, i.e., which correctly approximates the cost of the corresponding program; we identify the differences with recurrence relation systems, its possible applications and the new challenges that they bring about. Our general framework is illustrated by instantiating it to cost analysis of Java bytecode, Haskell, and Prolog.

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A theoretical study on the time analysis of programs

Cited by 7 publications

References 1 publication

On the Edge of Decidability in Complexity Analysis of Loop Programs

On the Edge of Decidability in Complexity Analysis of Loop Programs

Automatic complexity analysis

Cost Relation Systems: A Language-Independent Target Language for Cost Analysis

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