Roberto, Margherita and Beatrice

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A New Look at the Automatic Synthesis of Linear Ranking Functions

Fred Mesnard
LIM/IREMIA
Université de La Réeunion
Parc Technologique Universitaire
2, rue Joseph Wetzell - Bât 2
F-97490 Sainte Clotilde
La Réunion
France

Roberto Bagnara
BUGSENG and Dipartimento di Matematica e Informatica
Università di Parma
Parco Area delle Scienze 53/A
I-43124 Parma
Italy

Andrea Pescetti
Dipartimento di Matematica
Università di Parma
Parco Area delle Scienze 53/A
I-43124 Parma
Italy

Enea Zaffanella
Dipartimento di Matematica e Informatica
Università di Parma
Parco Area delle Scienze 53/A
I-43124 Parma
Italy

Abstract

The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many terminating loops admit one and algorithms exist to automatically synthesize it. In this paper we present two such algorithms: one based on work dated 1991 by Sohn and Van Gelder; the other, due to Podelski and Rybalchenko, dated 2004. Remarkably, while the two algorithms will synthesize a linear ranking function under exactly the same set of conditions, the former is mostly unknown to the community of termination analysis and its general applicability has never been put forward before the present paper. In this paper we thoroughly justify both algorithms, we prove their correctness, we compare their worst-case complexity and experimentally evaluate their efficiency, and we present an open-source implementation of them that will make it very easy to include termination-analysis capabilities in automatic program verifiers.


Available: PDF, 300 DPI, 600 DPI, and 1200 DPI PostScript, DVI, BibTeX entry.

[Page last updated on April 12, 2013, 18:30:32.]

© Roberto Bagnara
bagnara@cs.unipr.it

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