{"paper":{"title":"The subpower membership problem for bands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Markus Steindl","submitted_at":"2016-04-02T20:19:47Z","abstract_excerpt":"Fix a finite semigroup $S$ and let $a_1,\\ldots,a_k, b$ be tuples in a direct power $S^n$. The subpower membership problem (SMP) for $S$ asks whether $b$ can be generated by $a_1,\\ldots,a_k$. For bands (idempotent semigroups), we provide a dichotomy result: if a band $S$ belongs to a certain quasivariety, then $SMP(S)$ is in P; otherwise it is NP-complete.\n  Furthermore we determine the greatest variety of bands all of whose finite members induce a tractable SMP. Finally we present the first example of two finite algebras that generate the same variety and have tractable and NP-complete SMPs, r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01014","kind":"arxiv","version":1},"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"}