Joint spectral radius theory for automated complexity analysis of rewrite systems

Authors:
Aart Middeldorp;Georg Moser;Friedrich Neurauter;Johannes Waldmann;Harald Zankl
Affiliations:
Institute of Computer Science, University of Innsbruck, Austria;Institute of Computer Science, University of Innsbruck, Austria;Institute of Computer Science, University of Innsbruck, Austria;Fakultät Informatik, Mathematik und Naturwissenschaften, Hochschule für Technik, Wirtschaft und Kultur Leipzig, Germany;Institute of Computer Science, University of Innsbruck, Austria
Venue:
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Year:
2011

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Abstract

Matrix interpretations can be used to bound the derivational complexity of term rewrite systems. In particular, triangular matrix interpretations over the natural numbers are known to induce polynomial upper bounds on the derivational complexity of (compatible) rewrite systems. Recently two different improvements were proposed, based on the theory of weighted automata and linear algebra. In this paper we strengthen and unify these improvements by using joint spectral radius theory.