{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T02:57:08Z","timestamp":1775098628098,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:00:00Z","timestamp":1775088000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:00:00Z","timestamp":1775088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:00:00Z","timestamp":1775088000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2026,4,1]]},"abstract":"<jats:p>Myasnikov, Ushakov, and Won introduced power circuits in 2012 to construct a polynomial-time algorithm for the word problem in the Baumslag group, which has a non-elementary Dehn function. Power circuits are computational structures that support addition and the operation $(x,y) \\mapsto x \\cdot 2^y$ on integers. They also posed the question of decidability of the Diophantine problem over the structure $\\langle \\mathbb{N}_{&amp;gt;0}; +, x \\cdot 2^y, \\leq, 1 \\rangle$, which is closely related to power circuits. In this paper, we prove that the Diophantine problem over this structure is undecidable.<\/jats:p>\n                  <jats:p>Published in the journal of Groups, Complexity, Cryptology<\/jats:p>","DOI":"10.46298\/jgcc.2026.18.1.17270","type":"journal-article","created":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T02:10:10Z","timestamp":1775095810000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Diophantine problem related to power circuits"],"prefix":"10.46298","volume":"Volume 18, Issue 1, Special...","author":[{"given":"Alexander","family":"Rybalov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2026,4,2]]},"container-title":["journal of Groups, complexity, cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2601.00835v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2601.00835v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T02:10:11Z","timestamp":1775095811000},"score":1,"resource":{"primary":{"URL":"https:\/\/gcc.episciences.org\/17270"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,2]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/jgcc.2026.18.1.17270","relation":{"has-preprint":[{"id-type":"arxiv","id":"2601.00835v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2601.00835","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2601.00835","asserted-by":"subject"}]},"ISSN":["1869-6104"],"issn-type":[{"value":"1869-6104","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,2]]},"article-number":"17270"}}