{"paper":{"title":"Automated Tail Bound Analysis for Probabilistic Recurrence Relations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amir Kafshdar Goharshady, Hongfei Fu, Krishnendu Chatterjee, Yican Sun","submitted_at":"2023-05-24T12:47:50Z","abstract_excerpt":"Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit $\\kappa$, we consider the classical concept of tail probability $\\Pr[T \\ge \\kappa]$, i.e., the probability that the randomized runtime $T$ of the PRR exceeds the time limit $\\kappa$. Our focus is the formal analysis of tail bounds that aims at finding a tight asymptotic upper bound $u \\geq \\Pr[T\\ge\\kappa]$ in the time limit $\\kappa$. To address this problem, the classical and most well-known approach is the cookbook method by Karp (JACM 1994), wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.15104","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.15104/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"}