We study how the adoption of an evaluation mechanism with sharing and memoization impacts the class of functions which can be computed in polynomial time. We first show how a natural cost model in which lookup for an already computed result has no cost is indeed invariant. As a corollary, we then prove that the most general notion of ramified recurrence is sound for polynomial time, this way settling an open problem in implicit computational complexity.
@InProceedings{avanzini_et_al:LIPIcs.STACS.2015.62, author = {Avanzini, Martin and Dal Lago, Ugo}, title = {{On Sharing, Memoization, and Polynomial Time}}, booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)}, pages = {62--75}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-78-1}, ISSN = {1868-8969}, year = {2015}, volume = {30}, editor = {Mayr, Ernst W. and Ollinger, Nicolas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.62}, URN = {urn:nbn:de:0030-drops-49042}, doi = {10.4230/LIPIcs.STACS.2015.62}, annote = {Keywords: implicit computational complexity, data-tiering, polynomial time} }
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