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  • image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao

    One of the major open problems in complexity theory is proving superlogarithmic lower bounds on the depth of circuits (i.e., P ... NC1). This problem is interesting for two reasons: first, it is tightly related to understanding the power of parallel computation and of small-space computation, second, it is one of the first milestones toward proving superpolynomial circuit lower bounds. Karchmer, Raz, and Wigderson [Comput. Complexity, 5 (1995), pp. 191-204] suggested approaching this problem by proving the following conjecture: given two Boolean functions f and g, the depth complexity of the composed function g ... f is roughly the sum of the depth complexities of f and g. They showed that the validity of this conjecture would imply that P ... NC1. As a starting point for studying the composition of functions, they introduced a relation called 'the universal relation' and suggested studying the composition of universal relations.

    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Repository of the Cz...arrow_drop_down
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    SIAM Journal on Computing
    Article . 2017 . Peer-reviewed
    Data sources: Crossref
    addClaim

    This Research product is the result of merged Research products in OpenAIRE.

    You have already added works in your ORCID record related to the merged Research product.
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    citations6
    popularityAverage
    influenceAverage
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      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Repository of the Cz...arrow_drop_down
      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      SIAM Journal on Computing
      Article . 2017 . Peer-reviewed
      Data sources: Crossref
      addClaim

      This Research product is the result of merged Research products in OpenAIRE.

      You have already added works in your ORCID record related to the merged Research product.
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  • image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao

    One of the major open problems in complexity theory is proving superlogarithmic lower bounds on the depth of circuits (i.e., P ... NC1). This problem is interesting for two reasons: first, it is tightly related to understanding the power of parallel computation and of small-space computation, second, it is one of the first milestones toward proving superpolynomial circuit lower bounds. Karchmer, Raz, and Wigderson [Comput. Complexity, 5 (1995), pp. 191-204] suggested approaching this problem by proving the following conjecture: given two Boolean functions f and g, the depth complexity of the composed function g ... f is roughly the sum of the depth complexities of f and g. They showed that the validity of this conjecture would imply that P ... NC1. As a starting point for studying the composition of functions, they introduced a relation called 'the universal relation' and suggested studying the composition of universal relations.

    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Repository of the Cz...arrow_drop_down
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    SIAM Journal on Computing
    Article . 2017 . Peer-reviewed
    Data sources: Crossref
    addClaim

    This Research product is the result of merged Research products in OpenAIRE.

    You have already added works in your ORCID record related to the merged Research product.
    6
    citations6
    popularityAverage
    influenceAverage
    impulseAverage
    BIP!Powered by BIP!
    more_vert
      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Repository of the Cz...arrow_drop_down
      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      SIAM Journal on Computing
      Article . 2017 . Peer-reviewed
      Data sources: Crossref
      addClaim

      This Research product is the result of merged Research products in OpenAIRE.

      You have already added works in your ORCID record related to the merged Research product.
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