Bounding the Computational Complexity of Flowchart Programs with Multi-dimensional Rankings

Abstract : Proving the termination of a flowchart program can be done by exhibiting a ranking function, i.e., a function from the program states to a well-founded set, which strictly decreases at each program step. A standard method to automatically generate such a function is to compute invariants for each program point and to search for a ranking in a restricted class of functions that can be handled with linear programming techniques. Our first contribution is to propose an efficient algorithm to compute ranking functions: It can handle flowcharts of arbitrary structure, the class of candidate rankings it explores is larger, and our method, although greedy, is provably complete. Our second contribution is to show how to use the ranking functions we generate to get upper bounds for the computational complexity (number of transitions) of the source program, again for flowcharts of arbitrary structure. This estimate is a polynomial, which means that we can handle programs with more than linear complexity. We applied the method on a collection of test cases from the literature. We also point out important extensions, mainly to do with the scalability of the algorithm and, in particular, the integration of techniques based on cutpoints.
Complete list of metadatas

Cited literature [33 references]  Display  Hide  Download

https://hal.inria.fr/inria-00464356
Contributor : Christophe Alias <>
Submitted on : Tuesday, March 16, 2010 - 6:53:58 PM
Last modification on : Saturday, March 30, 2019 - 1:32:13 AM
Long-term archiving on : Friday, June 18, 2010 - 11:26:25 PM

File

RR-7235.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00464356, version 1

Citation

Christophe Alias, Alain Darte, Paul Feautrier, Laure Gonnord. Bounding the Computational Complexity of Flowchart Programs with Multi-dimensional Rankings. [Research Report] RR-7235, INRIA. 2010, pp.32. ⟨inria-00464356⟩

Share

Metrics

Record views

473

Files downloads

382