LIPIcs.FSTTCS.2008.1762.pdf
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Complexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2008-12-05
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Georg Moser, Andreas Schnabl, and Johannes Waldmann. Complexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 304-315, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1762
https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1762
Abstract
For a given (terminating) term rewriting system
one can often estimate its \emph{derivational complexity} indirectly
by looking at the proof method that established termination. In this
spirit we investigate two instances of the interpretation method:
\emph{matrix interpretations} and \emph{context dependent interpretations}.
We introduce a subclass of matrix interpretations, denoted
as \emph{triangular matrix interpretations}, which induce
polynomial derivational complexity and establish tight correspondence
results between a subclass of context dependent interpretations and
restricted triangular matrix interpretations.
The thus obtained new results are easy to implement and
considerably extend the analytic power of existing results.
We provide ample numerical data for assessing the viability of the method.
Keywords
- Term Rewriting
- Derivational Complexity
- Termination
- Automation
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