{"abstracts":[{"sha1":"aca6eab59a3866f8f96019791047661bc9ccf921","content":"For decision problems P defined over Boolean circuits from a restricted set\nof gates, we have that P(B) AC0 many-one reduces to P(B') for all finite sets B\nand B' of gates such that all gates from B can be computed by circuits over\ngates from B'. In this paper, we show that a weaker version of this statement\nholds for decision problems defined over Boolean formulae, namely that P(B) NC2\nmany-one reduces to P(B' union and,or) and that P(B) NC2 many-one reduces to\nP(B' union false,true), for all finite sets B and B' of Boolean functions\nsuch that all f in B can be defined in B'.","mimetype":"text/plain","lang":"en"},{"sha1":"7f99cb530df02326dfad9dfba092077926eb1a84","content":"For decision problems P defined over Boolean circuits from a restricted set\nof gates, we have that P(B) AC0 many-one reduces to P(B') for all finite sets B\nand B' of gates such that all gates from B can be computed by circuits over\ngates from B'. In this paper, we show that a weaker version of this statement\nholds for decision problems defined over Boolean formulae, namely that P(B) NC2\nmany-one reduces to P(B' union {and,or}) and that P(B) NC2 many-one reduces to\nP(B' union {false,true}), for all finite sets B and B' of Boolean functions\nsuch that all f in B can be defined in B'.","mimetype":"application/x-latex","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Michael Thomas","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v3","ext_ids":{"arxiv":"1007.2924v3"},"release_year":2012,"release_date":"2012-01-05","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["663gazskmfbqbei54grpu7yppa"],"mimetype":"application/pdf","urls":[{"url":"https://archive.org/download/arxiv-1007.2924/1007.2924.pdf","rel":"archive"}],"sha256":"65494aaf6e91cb31344d21acce2448ad73b2eaa76aa2a1dc165908b301621a89","sha1":"e39a7cdb7848a205f8e4eb8a420631d07d26bab0","md5":"301b648a0768ef25bf9aaa291a80b2cc","size":96469,"revision":"a2219650-a069-484c-9faf-93360259415f","ident":"nxgc4adfard5vhq674na7wyk4e","state":"active"}],"work_id":"wgaugm6xwrhorclebgovtw54ja","title":"On the Applicability of Post's Lattice","state":"active","ident":"663gazskmfbqbei54grpu7yppa","revision":"0970a9ed-2f69-43d1-8abd-4ca76af5c030","extra":{"arxiv":{"base_id":"1007.2924","categories":["cs.CC","cs.LO"]}}}