Targeting Completeness: Automated Complexity Analysis of Integer Programs

Fuente: arXiv
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Main Authors: Lommen, Nils, Meyer, Éléanore, Giesl, Jürgen
Format: Preprint
Published: 2024
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author Lommen, Nils
Meyer, Éléanore
Giesl, Jürgen
author_facet Lommen, Nils
Meyer, Éléanore
Giesl, Jürgen
contents There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops), where questions regarding the runtime and the size of variable values are decidable and where we can therefore obtain techniques that are complete for such subclasses. We show how to use these results for the complexity analysis of arbitrary general integer programs. To this end, we present a modular approach which computes local runtime and size bounds for subprograms which correspond to prs-loops. These local bounds are then lifted to global runtime and size bounds for the whole integer program. Furthermore, we introduce several techniques to transform larger programs into prs-loops to increase the scope of the approach. The power of the procedure is shown by our implementation in the complexity analysis tool KoAT.
format Preprint
id arxiv_https___arxiv_org_abs_2412_01832
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Targeting Completeness: Automated Complexity Analysis of Integer Programs
Lommen, Nils
Meyer, Éléanore
Giesl, Jürgen
Logic in Computer Science
There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops), where questions regarding the runtime and the size of variable values are decidable and where we can therefore obtain techniques that are complete for such subclasses. We show how to use these results for the complexity analysis of arbitrary general integer programs. To this end, we present a modular approach which computes local runtime and size bounds for subprograms which correspond to prs-loops. These local bounds are then lifted to global runtime and size bounds for the whole integer program. Furthermore, we introduce several techniques to transform larger programs into prs-loops to increase the scope of the approach. The power of the procedure is shown by our implementation in the complexity analysis tool KoAT.
title Targeting Completeness: Automated Complexity Analysis of Integer Programs
topic Logic in Computer Science
url https://arxiv.org/abs/2412.01832