{"paper":{"title":"Concentration Independent Random Number Generation in Tile Self-Assembly","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.ET"],"primary_cat":"cs.FL","authors_text":"Bin Fu, Cameron Chalk, Eric Martinez, Robert Schweller, Tim Wylie","submitted_at":"2015-06-01T21:32:37Z","abstract_excerpt":"In this paper we introduce the \\emph{robust random number generation} problem where the goal is to design an abstract tile assembly system (aTAM system) whose terminal assemblies can be split into $n$ partitions such that a resulting assembly of the system lies within each partition with probability 1/$n$, regardless of the relative concentration assignment of the tile types in the system. First, we show this is possible for $n=2$ (a \\emph{robust fair coin flip}) within the aTAM, and that such systems guarantee a worst case $\\mathcal{O}(1)$ space usage. We accompany our primary construction wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00680","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"}