{"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"}