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For each symbol $i$, we have that $Y_i = X_i$ with probability $1-\\eps$ and otherwise $Y_i$ is chosen independently and uniformly from $[s]$.\n  Alice and Bob wish to use their respective strings to extract a uniformly chosen common sequence from $[s]^k$ but without communicating. How well can they do? The trivial strategy of outputting the first $k$ symbols yields an agreement probability of $(1 - \\eps + \\eps/s)^k$. In a recent work by Bogdanov"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.5946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-08-29T15:27:35Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9def21216be1461b554f42d826c94bda52edf734adef648790b4134f87e5f91d","abstract_canon_sha256":"9f3c364e86fd95cf56f3f47e99ad6e921b85cdb3147ea074c5af096c7484ea60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:48.256363Z","signature_b64":"ac6ME/19s1mVIi67D9CEGxhAqsQ12HcxcS/IDFW3YbhDjQF2JsezcTkaB08vuS5itxW38Bc7s/EcqjmM1L6HDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d85f26eaca0c1f70a529a3a3c4fb8ad4e002e9cb14211840f27f54d6801be5e","last_reissued_at":"2026-05-18T03:46:48.255637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:48.255637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On extracting common random bits from correlated sources on large alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Elchanan Mossel, Joe Neeman, Siu On Chan","submitted_at":"2012-08-29T15:27:35Z","abstract_excerpt":"Suppose Alice and Bob receive strings $X=(X_1,...,X_n)$ and $Y=(Y_1,...,Y_n)$ each uniformly random in $[s]^n$ but so that $X$ and $Y$ are correlated . 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