{"paper":{"title":"The Compilability Thresholds of 2-CNF to OBDD","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO","math.PR"],"primary_cat":"cs.DS","authors_text":"Alexis de Colnet, Alfons Laarman, Joon Hyung Lee","submitted_at":"2026-03-16T15:59:34Z","abstract_excerpt":"We prove the existence of two thresholds regarding the compilability of random 2-CNF formulas to OBDDs. The formulas are drawn from $\\mathcal{F}_2(n,\\delta n)$, the uniform distribution over all 2-CNFs with $\\delta n$ clauses and $n$ variables, with $\\delta \\geq 0$ a constant. We show that, with high probability, the random 2-CNF admits OBDDs of size polynomial in $n$ if $0 \\leq \\delta < 1/2$ or if $\\delta > 1$. On the other hand, for $1/2 < \\delta < 1$, with high probability, the random $2$-CNF admits only OBDDs of size exponential in $n$. It is no coincidence that the two ``compilability thr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.15463","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.15463/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}