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Algorithms with polynomial interpretation termination proof

Published online by Cambridge University Press:  26 March 2001

G. BONFANTE
Affiliation:
Loria, Calligramme project, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France; (e-mail: bonfante@loria.fr, cichon@loria.fr, marionjy@loria.fr)
A. CICHON
Affiliation:
Loria, Calligramme project, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France; (e-mail: bonfante@loria.fr, cichon@loria.fr, marionjy@loria.fr)
J.-Y. MARION
Affiliation:
Loria, Calligramme project, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France; (e-mail: bonfante@loria.fr, cichon@loria.fr, marionjy@loria.fr)
H. TOUZET
Affiliation:
LIFL - USTL, 59655 Villeneuve d'Ascq Cedex, France; (e-mail: touzet@lifl.fr)
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Abstract

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We study the effect of polynomial interpretation termination proofs of deterministic (resp. non-deterministic) algorithms defined by con uent (resp. non-con uent) rewrite systems over data structures which include strings, lists and trees, and we classify them according to the interpretations of the constructors. This leads to the definition of six function classes which turn out to be exactly the deterministic (resp. non-deterministic) polynomial time, linear exponential time and linear doubly exponential time computable functions when the class is based on con uent (resp. non-con uent) rewrite systems. We also obtain a characterisation of the linear space computable functions. Finally, we demonstrate that functions with exponential interpretation termination proofs are super-elementary.

Type
Research Article
Copyright
© 2001 Cambridge University Press
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