{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QZPYMSKMG5F34EF4OETGHNW5WT","short_pith_number":"pith:QZPYMSKM","schema_version":"1.0","canonical_sha256":"865f86494c374bbe10bc712663b6ddb4f8c5ff2895af74356365bce5236d0622","source":{"kind":"arxiv","id":"1602.02743","version":1},"attestation_state":"computed","paper":{"title":"The IMP game: Learnability, approximability and adversarial learning beyond $\\Sigma^0_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CC","cs.FL"],"primary_cat":"cs.LO","authors_text":"David L. Dowe, Michael Brand","submitted_at":"2016-02-07T04:17:17Z","abstract_excerpt":"We introduce a problem set-up we call the Iterated Matching Pennies (IMP) game and show that it is a powerful framework for the study of three problems: adversarial learnability, conventional (i.e., non-adversarial) learnability and approximability. Using it, we are able to derive the following theorems. (1) It is possible to learn by example all of $\\Sigma^0_1 \\cup \\Pi^0_1$ as well as some supersets; (2) in adversarial learning (which we describe as a pursuit-evasion game), the pursuer has a winning strategy (in other words, $\\Sigma^0_1$ can be learned adversarially, but $\\Pi^0_1$ not); (3) s"},"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":"1602.02743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-02-07T04:17:17Z","cross_cats_sorted":["cs.AI","cs.CC","cs.FL"],"title_canon_sha256":"6d3350f6b9e9915414275ab0ed3f1c17a16f85ec335c2e1a2162ad83d52c9c88","abstract_canon_sha256":"f3ec69cd9c0af3681c230b8a4c4b2ab446fe9eb1da43d50d2d42a6f9e158168d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:08.215263Z","signature_b64":"EeATFt5GYGCnVg/JcY1aLdWXeT18DXmMe6rZcpVjPP0RZRmy/s7lKdAT2jKXJzg47wtY0xopchNoUOsuezDvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"865f86494c374bbe10bc712663b6ddb4f8c5ff2895af74356365bce5236d0622","last_reissued_at":"2026-05-18T01:21:08.214656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:08.214656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The IMP game: Learnability, approximability and adversarial learning beyond $\\Sigma^0_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CC","cs.FL"],"primary_cat":"cs.LO","authors_text":"David L. Dowe, Michael Brand","submitted_at":"2016-02-07T04:17:17Z","abstract_excerpt":"We introduce a problem set-up we call the Iterated Matching Pennies (IMP) game and show that it is a powerful framework for the study of three problems: adversarial learnability, conventional (i.e., non-adversarial) learnability and approximability. Using it, we are able to derive the following theorems. (1) It is possible to learn by example all of $\\Sigma^0_1 \\cup \\Pi^0_1$ as well as some supersets; (2) in adversarial learning (which we describe as a pursuit-evasion game), the pursuer has a winning strategy (in other words, $\\Sigma^0_1$ can be learned adversarially, but $\\Pi^0_1$ not); (3) s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02743","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.02743","created_at":"2026-05-18T01:21:08.214746+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.02743v1","created_at":"2026-05-18T01:21:08.214746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02743","created_at":"2026-05-18T01:21:08.214746+00:00"},{"alias_kind":"pith_short_12","alias_value":"QZPYMSKMG5F3","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"QZPYMSKMG5F34EF4","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"QZPYMSKM","created_at":"2026-05-18T12:30:41.710351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT","json":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT.json","graph_json":"https://pith.science/api/pith-number/QZPYMSKMG5F34EF4OETGHNW5WT/graph.json","events_json":"https://pith.science/api/pith-number/QZPYMSKMG5F34EF4OETGHNW5WT/events.json","paper":"https://pith.science/paper/QZPYMSKM"},"agent_actions":{"view_html":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT","download_json":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT.json","view_paper":"https://pith.science/paper/QZPYMSKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.02743&json=true","fetch_graph":"https://pith.science/api/pith-number/QZPYMSKMG5F34EF4OETGHNW5WT/graph.json","fetch_events":"https://pith.science/api/pith-number/QZPYMSKMG5F34EF4OETGHNW5WT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT/action/storage_attestation","attest_author":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT/action/author_attestation","sign_citation":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT/action/citation_signature","submit_replication":"https://pith.science/pith/QZPYMSKMG5F34EF4OETGHNW5WT/action/replication_record"}},"created_at":"2026-05-18T01:21:08.214746+00:00","updated_at":"2026-05-18T01:21:08.214746+00:00"}