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We also prove that the substitution basis defined by these three operations is minimal. Furthermore, we discuss alternative substitution bases under arity constraints.<\/jats:p>","DOI":"10.1093\/logcom\/exag010","type":"journal-article","created":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T12:35:24Z","timestamp":1770726924000},"source":"Crossref","is-referenced-by-count":0,"title":["A minimal substitution basis for the Kalm\u00e1r elementary functions"],"prefix":"10.1093","volume":"36","author":[{"given":"Mihai","family":"Prunescu","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Research Center for Logic, Optimization and Security (LOS), University of Bucharest , RO-010014 Bucharest ,","place":["Romania"]},{"name":"Simion Stoilow Institute of Mathematics of the Romanian Academy , Research unit 5, P. O. 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