{"paper":{"title":"On the Power of Many One-Bit Provers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Johan H{\\aa}stad, Per Austrin, Rafael Pass","submitted_at":"2013-01-12T23:02:05Z","abstract_excerpt":"We study the class of languages, denoted by $\\MIP[k, 1-\\epsilon, s]$, which have $k$-prover games where each prover just sends a \\emph{single} bit, with completeness $1-\\epsilon$ and soundness error $s$. For the case that $k=1$ (i.e., for the case of interactive proofs), Goldreich, Vadhan and Wigderson ({\\em Computational Complexity'02}) demonstrate that $\\SZK$ exactly characterizes languages having 1-bit proof systems with\"non-trivial\" soundness (i.e., $1/2 < s \\leq 1-2\\epsilon$). We demonstrate that for the case that $k\\geq 2$, 1-bit $k$-prover games exhibit a significantly richer structure:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2729","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"}