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Some New Consequences of the Hypothesis That P Has Fixed Polynomial-Size Circuits

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Theory and Applications of Models of Computation (TAMC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9076))

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Abstract

We present some new consequences of the hypothesis that \(\mathbf {P}\) can be computed by fixed polynomial-size circuits since [Lipton SCTC 94]. For instance, we show that the hypothesis implies that some small circuit family and BPP machines cannot be fooled by any complexity-theoretic pseudorandom generator \(G: \{0,1\}^{\varTheta (\log n)}\) to \(\{0,1\}^{n}\), which means the known derandomization argument of \(\mathbf {BPP}=\mathbf {P}\) no longer works. It also implies the existence of 2-round public-coin zero-knowledge proofs for \(\mathbf {NP}\).

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Acknowledgments

The author is grateful to the reviewers of TAMC 2015 for their detailed and useful comments. This work is supported by the National Natural Science Foundation of China (Grant No. 61100209) and Doctoral Fund of Ministry of Education of China (Grant No. 20120073110094).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Ning Ding

  2. NTT Secure Platform Laboratories, Tokyo, Japan

    Ning Ding

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  1. Ning Ding
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Correspondence to Ning Ding .

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Editors and Affiliations

  1. National University of Singapore, Singapore, Singapore

    Rahul Jain

  2. National University of Singapore, Singapore, Singapore

    Sanjay Jain

  3. National University of Singapore, Singapore, Singapore

    Frank Stephan

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Ding, N. (2015). Some New Consequences of the Hypothesis That P Has Fixed Polynomial-Size Circuits. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_8

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  • DOI: https://doi.org/10.1007/978-3-319-17142-5_8

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