{"paper":{"title":"Do CFLOBDDs Actually Make Use of Linear Structure?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Linear structure works with hierarchy in CFLOBDDs to enable efficient Boolean function compression.","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Meghana Aparna Sistla, Swarat Chaudhuri, Thomas W. Reps","submitted_at":"2026-05-15T02:45:02Z","abstract_excerpt":"Binary Decision Diagrams (BDDs) are a widely used data structure for efficient Boolean function representation. Context-Free-Language Ordered Binary Decision Diagrams (CFLOBDDs) are a recently introduced hierarchical data structure that can, in the best case, exhibit exponential compression over BDDs and double-exponential compression over decision trees. Roughly speaking, a CFLOBDD is a finite, acyclic, non-recursive hierarchical finite-state machine (HFSM) (with some additional restrictions). In this paper, we investigate the role of \\emph{linear structure} in CFLOBDDs -- a property that con"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We demonstrate that linear structure, in conjunction with hierarchical structure, plays a crucial role in enabling CFLOBDDs to achieve efficient function compression. Furthermore, we show that removing linearity from CFLOBDDs leads to a significant blowup in representation size, resulting in degraded performance in the domain of quantum-circuit simulation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That modifications removing linearity from CFLOBDDs isolate the effect of linear structure without altering other representational properties or implementation details that could independently affect size and performance.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Linear structure combined with hierarchy is crucial for CFLOBDD compression efficiency; its removal produces significant blowup and degraded results in quantum simulation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Linear structure works with hierarchy in CFLOBDDs to enable efficient Boolean function compression.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a4ee39fab8b9eff9bfc5f55d11ae3fd23f38b0995d2eba9003d08096f2648f06"},"source":{"id":"2605.15552","kind":"arxiv","version":1},"verdict":{"id":"b82384e1-ca0a-4ade-9688-0b57e369dc55","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:44:01.685786Z","strongest_claim":"We demonstrate that linear structure, in conjunction with hierarchical structure, plays a crucial role in enabling CFLOBDDs to achieve efficient function compression. Furthermore, we show that removing linearity from CFLOBDDs leads to a significant blowup in representation size, resulting in degraded performance in the domain of quantum-circuit simulation.","one_line_summary":"Linear structure combined with hierarchy is crucial for CFLOBDD compression efficiency; its removal produces significant blowup and degraded results in quantum simulation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That modifications removing linearity from CFLOBDDs isolate the effect of linear structure without altering other representational properties or implementation details that could independently affect size and performance.","pith_extraction_headline":"Linear structure works with hierarchy in CFLOBDDs to enable efficient Boolean function compression."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15552/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:34:36.245952Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:19.030538Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:52:17.685139Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:41:56.093985Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"48be86fae37609743341194b438de1cd5836eb5905077a546e4e549f5f8ef95f"},"references":{"count":21,"sample":[{"doi":"","year":2005,"title":"Reps, and Mihalis Yannakakis","work_id":"ecb306ee-6d8f-4c84-a028-100c1ce36787","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Rajeev Alur and Parthasarathy Madhusudan. 2009. Adding nesting structure to words.Journal of the ACM (JACM)56, 3 (2009), 1–43","work_id":"268cef0d-b9aa-4517-bb05-1976a8a8f1cb","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"Anuchit Anuchitanukul, Zohar Manna, and Tomás E. Uribe. 1995. Differential BDDs. InComputer Science Today: Recent Trends and Developments (Lecture Notes in Computer Science, Vol. 1000), J. van Leeuwen","work_id":"c5ce85d8-8779-473d-bbad-a42f58949ea0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Iris Bahar, Erica A","work_id":"0fdc3b47-6496-4e21-8744-fc5f6cfd4df1","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1023/a:1008699807402","year":1997,"title":"Des.10, 2/3 (1997), 171–206","work_id":"380584b7-f7dd-4277-8ad1-134bc579dce7","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":21,"snapshot_sha256":"7f0edb663e3f331243bd56425eb9a3c37c87483eedfef49fe920bd0ea6c344a2","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"}