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On the Formalization of Termination Techniques based on Multiset Orderings

René Thiemann, Guillaume Allais, and Julian Nagele

Proceedings of the 23rd International Conference on Rewriting Techniques and Applications (RTA 2012), Leibniz International Proceedings in Informatics 15, pp. 339 – 354, 2012.

Abstract

Multiset orderings are a key ingredient in certain termination techniques like the recursive path ordering and a variant of size-change termination. In order to integrate these techniques in a certifier for termination proofs, we have added them to the Isabelle Formalization of Rewriting. To this end, it was required to extend the existing formalization on multiset orderings towards a generalized multiset ordering. Afterwards, the soundness proofs of both techniques have been established, although only after fixing some definitions. Concerning efficiency, it is known that the search for suitable parameters for both techniques is NP-hard. We show that checking the correct application of the techniques – where all parameters are provided – is also NP-hard, since the problem of deciding the generalized multiset ordering is NP-hard.

 

  PDF |    doi:10.4230/LIPIcs.RTA.2012.339  |  © Creative Commons License – NC – ND

BibTeX 

@inproceedings{RTGAJN-RTA12,
author = "Ren\'{e} Thiemann and Guillaume Allais and Julian Nagele",
title = "On the Formalization of Termination Techniques based on Multiset Orderings",
booktitle = "Proceedings of the 23rd International Conference on Rewriting
Techniques and Applications",
series = "Leibniz International Proceedings in Informatics",
volume = 15,
pages = "339--354",
year = 2012
}
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