We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational linear recurrence sequence and computes effective fine-grained lower bounds on the growth rate of the sequence.
@InProceedings{almagor_et_al:LIPIcs.CONCUR.2018.42, author = {Almagor, Shaull and Chapman, Brynmor and Hosseini, Mehran and Ouaknine, Jo\"{e}l and Worrell, James}, title = {{Effective Divergence Analysis for Linear Recurrence Sequences}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {42:1--42:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.42}, URN = {urn:nbn:de:0030-drops-95802}, doi = {10.4230/LIPIcs.CONCUR.2018.42}, annote = {Keywords: Linear recurrence sequences, Divergence, Algebraic numbers, Positivity} }
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