{"paper":{"title":"Characterization and Lower Bounds for Branching Program Size using Projective Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jayalal Sarma, Krishnamoorthy Dinesh, Sajin Koroth","submitted_at":"2016-04-25T11:04:39Z","abstract_excerpt":"We study projective dimension, a graph parameter (denoted by pd$(G)$ for a graph $G$), introduced by (Pudl\\'ak, R\\\"odl 1992), who showed that proving lower bounds for pd$(G_f)$ for bipartite graphs $G_f$ associated with a Boolean function $f$ imply size lower bounds for branching programs computing $f$. Despite several attempts (Pudl\\'ak, R\\\"odl 1992 ; Babai, R\\'{o}nyai, Ganapathy 2000), proving super-linear lower bounds for projective dimension of explicit families of graphs has remained elusive.\n  We show that there exist a Boolean function $f$ (on $n$ bits) for which the gap between the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07200","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/1604.07200/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"}