{"paper":{"title":"Finite Bases with Respect to the Superposition in Classes of Elementary Recursive Functions, dissertation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Sergey Volkov","submitted_at":"2016-11-14T11:34:55Z","abstract_excerpt":"This is a thesis that was defended in 2009 at Lomonosov Moscow State University.\n  In Chapter 1:\n  1. It is proved that that the class of lower (Skolem) elementary functions is the set of all polynomial-bounded functions that can be obtained by a composition of $x+1$, $xy$, $\\max(x-y,0)$, $x\\wedge y$, $\\lfloor x/y \\rfloor$, and one exponential function ($2^x$ or $x^y$) using formulas that have no more than 2 floors with respect to an exponent (for example, $(x+y)^{xy+z}+1$ has 2 floors, $2^{2^x}$ has 3 floors). Here $x\\wedge y$ is a bitwise AND of $x$ and $y$.\n  2. It is proved that $\\{x+y,\\ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04843","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}