{"paper":{"title":"Sensitivity, Affine Transforms and Quantum Communication Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jayalal Sarma, Krishnamoorthy Dinesh","submitted_at":"2018-08-30T09:09:30Z","abstract_excerpt":"$\\newcommand{\\F}{\\mathbb{F}}$We study the Boolean function parameters sensitivity ($s$), block sensitivity ($bs$), and alternation ($alt$) under specially designed affine transforms. For a function $f:\\F_2^n\\to \\{0,1\\}$, and $A=Mx+b$ for $M \\in \\F_2^{n\\times n}$ and $b\\in \\F_2^n$, the result of the transformation $g$ is defined as $\\forall x\\in\\F_2^n, g(x)=f(Mx+b)$.\n  We study alternation under linear shifts ($M$ is the identity matrix) called the shift invariant alternation (denoted by $salt(f)$). We exhibit an explicit family of functions for which $salt(f)$ is $2^{\\Omega(s(f))}$. We show an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10191","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.10191/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}