{"paper":{"title":"The Post correspondence problem in groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"math.GR","authors_text":"Alexander Ushakov, Alexei Myasnikov, Andrey Nikolaev","submitted_at":"2013-10-19T16:47:48Z","abstract_excerpt":"We generalize the classical Post correspondence problem ($\\mathbf{PCP}_n$) and its non-homogeneous variation ($\\mathbf{GPCP}_n$) to non-commutative groups and study the computational complexity of these new problems. We observe that $\\mathbf{PCP}_n$ is closely related to the equalizer problem in groups, while $\\mathbf{GPCP}_n$ is connected to the double twisted conjugacy problem for endomorphisms. Furthermore, it is shown that one of the strongest forms of the word problem in a group $G$ (we call it the {\\em hereditary word problem}) can be reduced to $\\mathbf{GPCP}_n$ in $G$ in polynomial tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5246","kind":"arxiv","version":2},"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"}