{"paper":{"title":"On the Complexity of Language Membership for Probabilistic Words","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Antoine Amarilli, Mika\\\"el Monet, Paul Rapha\\\"el, Sylvain Salvati","submitted_at":"2025-10-09T12:13:34Z","abstract_excerpt":"We study the membership problem to context-free languages (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters. Our task is to compute, given a probabilistic word, what is the probability that a word drawn according to the distribution belongs to the language $L$. This problem generalizes the problem of counting how many words of length $n$ belong to $L$, or of counting how many completions of a partial word belong to $L$.\n  We show that this problem is in polynomial time for unambiguous context-free languages (uCFLs), but can be #P-hard alrea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.08127","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/2510.08127/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"}