{"paper":{"title":"On the cost of simulating a parallel Boolean automata network by a block-sequential one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.DM","authors_text":"Florian Bridoux, Guillaume Theyssier, K\\'evin Perrot, Pierre Guillon, Sylvain Sen\\'e","submitted_at":"2017-02-10T08:52:51Z","abstract_excerpt":"In this article we study the minimum number $\\kappa$ of additional automata that a Boolean automata network (BAN) associated with a given block-sequential update schedule needs in order to simulate a given BAN with a parallel update schedule. We introduce a graph that we call $\\mathsf{NECC}$ graph built from the BAN and the update schedule. We show the relation between $\\kappa$ and the chromatic number of the $\\mathsf{NECC}$ graph. Thanks to this $\\mathsf{NECC}$ graph, we bound $\\kappa$ in the worst case between $n/2$ and $2n/3+2$ ($n$ being the size of the BAN simulated) and we conjecture tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03101","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"}