{"paper":{"title":"A complexity theory of constructible functions and sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.LO"],"primary_cat":"math.AG","authors_text":"Saugata Basu","submitted_at":"2013-09-23T18:21:18Z","abstract_excerpt":"In this paper we introduce constructible analogs of the discrete complexity classes $\\mathbf{VP}$ and $\\mathbf{VNP}$ of sequences of functions. The functions in the new definitions are constructible functions on $\\mathbb{R}^n$ or $\\mathbb{C}^n$. We define a class of sequences of constructible functions that play a role analogous to that of $\\mathbf{VP}$ in the more classical theory. The class analogous to $\\mathbf{VNP}$ is defined using Euler integration. We discuss several examples, develop a theory of completeness, and pose a conjecture analogous to the $\\mathbf{VP}$ vs. $\\mathbf{VNP}$ conje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5905","kind":"arxiv","version":6},"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"}