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The syntactic complexity of a subclass of regular languages is the worst-case syntactic complexity taken as a function of the state complexity $n$ of languages in that class. We prove that $n^{n-1}$, $n^{n-1}+n-1$, and $n^{n-2}+(n-2)2^{n-2}+1$ are tight upper bounds on the syntactic complexities of right ideals and prefix-closed languages, left ideals and suffix-closed"},"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":"1509.06032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-09-20T17:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"58a217696ecf92127ef91a81aca0685024c13de36750628f816c17aad6c534c2","abstract_canon_sha256":"cf9574f3451f17f8a5a0ab5d526d3ccc38eb2839403a9c86d826ce9b024ab8af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:55.537113Z","signature_b64":"nZEdRFp48Zw71Uo9/ydD+UJigTImUzsfiNFe/shbCq59IpGTzJJ5yAnde7fp9faW1Y4NLbWGhegdxhjL81U0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b809c8e9dc5190baa06cc588fc19f0379903ab433ce87f5dc4763146b575efc7","last_reissued_at":"2026-05-18T00:52:55.536547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:55.536547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Syntactic complexity of regular ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Janusz A. 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