{"paper":{"title":"A composition theorem for parity kill number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"John Wright, Li-Yang Tan, Ryan O'Donnell, Xiaorui Sun, Yu Zhao","submitted_at":"2013-12-07T21:40:43Z","abstract_excerpt":"In this work, we study the parity complexity measures ${\\mathsf{C}^{\\oplus}_{\\min}}[f]$ and ${\\mathsf{DT^{\\oplus}}}[f]$. ${\\mathsf{C}^{\\oplus}_{\\min}}[f]$ is the \\emph{parity kill number} of $f$, the fewest number of parities on the input variables one has to fix in order to \"kill\" $f$, i.e. to make it constant. ${\\mathsf{DT^{\\oplus}}}[f]$ is the depth of the shortest \\emph{parity decision tree} which computes $f$. These complexity measures have in recent years become increasingly important in the fields of communication complexity \\cite{ZS09, MO09, ZS10, TWXZ13} and pseudorandomness \\cite{BK1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2143","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"}