Number of the records: 1  

Amplifying lower bounds by means of self-reducibility

  1. 1.
    0352511 - MÚ 2011 RIV US eng J - Journal Article
    Allender, E. - Koucký, Michal
    Amplifying lower bounds by means of self-reducibility.
    Journal of the ACM. Roč. 57, č. 3 (2010), s. 1-36. ISSN 0004-5411. E-ISSN 1557-735X
    R&D Projects: GA ČR GAP202/10/0854; GA MŠMT(CZ) 1M0545; GA AV ČR IAA100190902
    Institutional research plan: CEZ:AV0Z10190503
    Keywords : Circuit Complexity * Lower Bounds * Natural Proofs * Self-Reducibility * Time-Space Tradeoffs
    Subject RIV: BA - General Mathematics
    Impact factor: 3.375, year: 2010
    http://dl.acm.org/citation.cfm?doid=1706591.1706594

    We observe that many important computational problems in NC^1 share a simple self-reducibility property. We then show that, for any problem A having this self-reducibility property, A has polynomial-size TC^0 circuits if and only if it has TC^0 circuits of size n^{1+eps} for every eps> 0 (counting the number of wires in a circuit as the size of the circuit). As an example of what this observation yields, consider the Boolean Formula Evaluation problem (BFE), which is complete for NC^1 and has the self-reducibility property. It follows from a lower bound of Impagliazzo, Paturi, and Saks, that BFE requires depth d TC^0 circuits of size n^{1+eps_d} . If one were able to improve this lower bound to show that there is some constant eps> 0 (independent of the depth d) such that every TC^0 circuit family recognizing BFE has size at least n^{1+eps}, then it would follow that TC^0 /not= NC^1.
    Permanent Link: http://hdl.handle.net/11104/0192003

     
    FileDownloadSizeCommentaryVersionAccess
    Koucky.pdf1249.6 KBAuthor’s postprintrequire
     
Number of the records: 1  

  This site uses cookies to make them easier to browse. Learn more about how we use cookies.