Proving loop termination: Beyond the traditional method.

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Bibliographic Details
Title:	Proving loop termination: Beyond the traditional method.
Authors:	Chen, Tennyson X.¹ chen@rti.org, Meyer, Martin D.¹
Source:	Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.). 2009 Supplement 2, Vol. 9, p169-S178. 10p. 1 Chart.
Subjects:	Loop tiling (Computer science), Iterative methods (Mathematics), Recursive functions, Recursive programming, Computer memory management
Abstract:	The traditional method for proving loop termination requires us to define a bound function of program variables. The criterion in this method is well-defined and can be easy to apply, as such functions are obvious for many loops. However in some cases, it can be very difficult to define a bound function. In this paper, we discuss how to prove loop termination by using alternative methods. First we show how to prove loop termination by solving a recursive relation that defines the number of iterations remaining in any execution state. Then we introduce a step-by-step approach for applying this recursive relation method. This new method can also be used to investigate preconditions that lead to loop termination in non-deterministic cases. Finally, we illustrate another method that uses a more general criterion for proving loop termination. The new criterion is a generalization of the classical one. This paper does not attempt to offer a one-size-fits-all approach. Rather, it provides some alternative methods that make proving loop termination easier in some cases, where termination might otherwise be difficult if not impossible to prove. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	The traditional method for proving loop termination requires us to define a bound function of program variables. The criterion in this method is well-defined and can be easy to apply, as such functions are obvious for many loops. However in some cases, it can be very difficult to define a bound function. In this paper, we discuss how to prove loop termination by using alternative methods. First we show how to prove loop termination by solving a recursive relation that defines the number of iterations remaining in any execution state. Then we introduce a step-by-step approach for applying this recursive relation method. This new method can also be used to investigate preconditions that lead to loop termination in non-deterministic cases. Finally, we illustrate another method that uses a more general criterion for proving loop termination. The new criterion is a generalization of the classical one. This paper does not attempt to offer a one-size-fits-all approach. Rather, it provides some alternative methods that make proving loop termination easier in some cases, where termination might otherwise be difficult if not impossible to prove. [ABSTRACT FROM AUTHOR]
ISSN:	14727978
DOI:	10.3233/JCM-2009-0245