{"paper":{"title":"Smallest Suffixient Sets: Effectiveness, Resilience, and Calculation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The size of the smallest suffixient set is at most linear in the number of Burrows-Wheeler runs and strictly smaller than the smallest lexicographic parse on some string families.","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.FL","authors_text":"Cristian Urbina, Giuseppe Romana, Gonzalo Navarro, Hiroto Fujimaru","submitted_at":"2025-06-05T23:58:03Z","abstract_excerpt":"A suffixient set is a novel combinatorial object that captures the essential information of repetitive strings in a way that, provided with a random access mechanism, supports various forms of pattern matching. In this paper, we study the size $\\chi$ of the smallest suffixient set as a repetitiveness measure.\n  First, we study its sensitivity to various string operations. We show that $\\chi$ cannot increase by more than 2 after appending or prepending a character to the string. As a consequence, we are able to give simple linear-time online algorithms to compute smallest suffixient sets. We al"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that χ = O(r) (where r is the number of runs in the Burrows-Wheeler Transform of the string), that there are string families where χ=o(v) (where v is the size of the smallest lexicographic parse of the string), and that χ ≤ σ+2 on episturmian words over alphabets of size σ.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The definition and utility of a suffixient set rests on the assumption that, provided with a random access mechanism, it supports various forms of pattern matching on the underlying repetitive string.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Smallest suffixient set size χ is O(r) for BWT runs r, o(v) for some lex parses, bounded by σ+2 on episturmian words, increases by at most 2 on append/prepend, and can increase by Ω(√n) under edits or rotations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The size of the smallest suffixient set is at most linear in the number of Burrows-Wheeler runs and strictly smaller than the smallest lexicographic parse on some string families.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ee2b46e2711ed47c1de21fe591b5ff73f3299d6213ecb4c88f3b7576791eaa00"},"source":{"id":"2506.05638","kind":"arxiv","version":6},"verdict":{"id":"d439ae4c-b031-48c8-8ea4-9192d26a39ce","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T10:59:09.352041Z","strongest_claim":"We show that χ = O(r) (where r is the number of runs in the Burrows-Wheeler Transform of the string), that there are string families where χ=o(v) (where v is the size of the smallest lexicographic parse of the string), and that χ ≤ σ+2 on episturmian words over alphabets of size σ.","one_line_summary":"Smallest suffixient set size χ is O(r) for BWT runs r, o(v) for some lex parses, bounded by σ+2 on episturmian words, increases by at most 2 on append/prepend, and can increase by Ω(√n) under edits or rotations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The definition and utility of a suffixient set rests on the assumption that, provided with a random access mechanism, it supports various forms of pattern matching on the underlying repetitive string.","pith_extraction_headline":"The size of the smallest suffixient set is at most linear in the number of Burrows-Wheeler runs and strictly smaller than the smallest lexicographic parse on some string families."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05638/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":2,"snapshot_sha256":"a7662297e5524a5edf8c4400a1810de5016ccd721bd1d1f2191e02f2b2b40e9b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}