In this short survey paper we state the Büchi conjecture and discuss its relations with the Hilbert Tenth Problem. We give some generalizations of the conjecture, and include some numerical examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-2, title = {The B\"uchi sequences and Hilbert's Tenth Problem}, journal = {Banach Center Publications}, volume = {108}, year = {2016}, pages = {23-30}, zbl = {06622282}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-2} }
(éd.). The Büchi sequences and Hilbert's Tenth Problem. Banach Center Publications, Tome 108 (2016) pp. 23-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-2/