In this paper we present a new path order for rewrite systems, the exponential path order EPO*. Suppose a term rewrite system is compatible with EPO*, then the runtime complexity of this rewrite system is bounded from above by an exponential function. Furthermore, the class of function computed by a rewrite system compatible with EPO* equals the class of functions computable in exponential time on a Turing machine.
@InProceedings{avanzini_et_al:LIPIcs.RTA.2011.123, author = {Avanzini, Martin and Eguchi, Naohi and Moser, Georg}, title = {{A Path Order for Rewrite Systems that Compute Exponential Time Functions}}, booktitle = {22nd International Conference on Rewriting Techniques and Applications (RTA'11)}, pages = {123--138}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-30-9}, ISSN = {1868-8969}, year = {2011}, volume = {10}, editor = {Schmidt-Schauss, Manfred}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2011.123}, URN = {urn:nbn:de:0030-drops-31127}, doi = {10.4230/LIPIcs.RTA.2011.123}, annote = {Keywords: Runtime Complexity, Exponential Time Functions, Implicit Computational Complexity} }
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