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Degree vs. approximate degree and quantum implications of Huang’s sensitivity theorem. (English) Zbl 07765252

Khuller, Samir (ed.) et al., Proceedings of the 53rd annual ACM SIGACT symposium on theory of computing, STOC ’21, virtual, Italy, June 21–25, 2021. New York, NY: Association for Computing Machinery (ACM). 1330-1342 (2021).

MSC:

68Qxx Theory of computing

References:

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[2] Scott Aaronson, Shalev Ben-David, Robin Kothari, Shravas Rao, and Avishay Tal. 2020. Degree vs. Approximate Degree and Quantum Implications of Huang’s Sensitivity Theorem. arXiv preprint arXiv:2010.12629, 2020.
[3] Scott Aaronson, Shalev Ben-David, Robin Kothari, and Avishay Tal. 2020. Quantum Implications of Huang’s Sensitivity Theorem. arXiv preprint arXiv:2004.13231, 2020.
[4] Andris Ambainis. 2002. Quantum Lower Bounds by Quantum Arguments. J. Comput. System Sci., 64, 4, jun, 2002. Pages 750-767. · Zbl 1015.68075 · doi:10.1006/jcss.2002.1826
[5] Andris Ambainis. 2013. Superlinear Advantage for Exact Quantum Algorithms. In Proceedings of the 45th ACM Symposium on Theory of Computing (STOC 2013). Pages 891-900. · Zbl 1293.68124 · doi:10.1145/2488608.2488721
[6] Andris Ambainis, Kaspars Balodis, Aleksandrs Belovs, Troy Lee, Miklos Santha, and Juris Smotrovs. 2017. Separations in Query Complexity Based on Pointer Functions. Journal of the ACM, 64, 5, Sept., 2017. · Zbl 1426.68109 · doi:10.1145/3106234
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[8] Nikhil Bansal and Makrand Sinha. 2020. k-Forrelation Optimally Separates Quantum and Classical Query Complexity. arXiv preprint arXiv:2008.07003, 2020.
[9] Howard Barnum and Michael Saks. 2004. A lower bound on the quantum query complexity of read-once functions. J. Comput. System Sci., 69, 2, 2004. Pages 244 - 258. · Zbl 1083.68045 · doi:10.1016/j.jcss.2004.02.002
[10] Howard Barnum, Michael E. Saks, and Mario Szegedy. 2003. Quantum query complexity and semi-definite programming. In 18th Annual IEEE Conference on Computational Complexity (Complexity 2003). Pages 179-193. · doi:10.1109/CCC.2003.1214419
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[63] Andris Ambainis. 2002. Quantum Lower Bounds by Quantum Arguments. J. Comput. System Sci., 64, 4, jun, 2002. Pages 750-767. · Zbl 1015.68075 · doi:10.1006/jcss.2002.1826
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[68] Howard Barnum and Michael Saks. 2004. A lower bound on the quantum query complexity of read-once functions. J. Comput. System Sci., 69, 2, 2004. Pages 244 - 258. · Zbl 1083.68045 · doi:10.1016/j.jcss.2004.02.002
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[72] Shalev Ben-David, Pooya Hatami, and Avishay Tal. 2017. Low-Sensitivity Functions from Unambiguous Certificates. In 8th Innovations in Theoretical Computer Science Conference, ITCS 2017. LIPIcs. 67, Schloss Dagstuhl - Leibniz-Zentrum für Informatik. Pages 28:1-28:23. · Zbl 1402.68082 · doi:10.4230/LIPIcs.ITCS.2017.28
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[74] Harry Buhrman, Richard Cleve, Ronald de Wolf, and Christof Zalka. 1999. Bounds for small-error and zero-error quantum algorithms. In 40th Annual Symposium on Foundations of Computer Science. Pages 358-368. · doi:10.1109/SFFCS.1999.814607
[75] Harry Buhrman and Ronald de Wolf. 2002. Complexity measures and decision tree complexity: a survey. Theoretical Computer Science, 288, 1, 2002. Pages 21-43. https://doi.org/10.1016/S0304-3975(01)00144-X · Zbl 1061.68058 · doi:10.1016/S0304-3975(01)00144-X
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[84] Chris Godsil and Gordon Royle. 2001. Algebraic Graph Theory. Springer New York. · Zbl 0968.05002 · doi:10.1007/978-1-4613-0163-9
[85] Mika Göös, T. S. Jayram, Toniann Pitassi, and Thomas Watson. 2018. Randomized Communication versus Partition Number. ACM Transactions on Computation Theory, 10, 1, Jan., 2018. · Zbl 1427.68083 · doi:10.1145/3170711
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[89] Hao Huang. 2019. Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture. Annals of Mathematics, 190, 3, 2019. Pages 949-955. · Zbl 1427.05116 · doi:10.4007/annals.2019.190.3.6
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[95] Sophie Laplante, Troy Lee, and Mario Szegedy. 2006. THE QUANTUM ADVERSARY METHOD AND CLASSICAL FORMULA SIZE LOWER BOUNDS. computational complexity, 15, 2, jun, 2006. Pages 163-196. · Zbl 1132.68032 · doi:10.1007/s00037-006-0212-7
[96] Troy Lee, Adi Shraibman, and Robert Spalek. 2008. A Direct Product Theorem for Discrepancy. In 23rd Annual IEEE Conference on Computational Complexity. · doi:10.1109/ccc.2008.25
[97] Nati Linial, Shahar Mendelson, Gideon Schechtman, and Adi Shraibman. 2007. Complexity measures of sign matrices. Combinatorica, 27, 4, 2007. Pages 439-463. · Zbl 1164.68006 · doi:10.1007/s00493-007-2160-5
[98] Frédéric Magniez, Miklos Santha, and Mario Szegedy. 2007. Quantum Algorithms for the Triangle Problem. SIAM J. Comput., 37, 2, 2007. Pages 413-424. · Zbl 1166.68032 · doi:10.1137/050643684
[99] Gatis Midrijanis. 2004. Exact quantum query complexity for total Boolean functions. arXiv preprint quant-ph/0403168, 2004.
[100] Noam Nisan. 1991. CREW PRAMs and Decision Trees. SIAM J. Comput., 20, 6, 1991. Pages 999-1007. · Zbl 0737.68028 · doi:10.1137/0220062
[101] Noam Nisan and Mario Szegedy. 1994. On the Degree of Boolean Functions as Real Polynomials. Computational Complexity, 4, 4, 1994. Pages 301-313. · Zbl 0829.68047 · doi:10.1007/BF01263419
[102] Noam Nisan and Avi Wigderson. 1995. On rank vs. communication complexity. Combinatorica, 15, 4, 1995. Pages 557-565. · Zbl 0845.68038 · doi:10.1007/BF01192527
[103] Ryan O’Donnell. 2009. Analysis of Boolean Functions. Cambridge University Press. · doi:10.1017/cbo9781139814782
[104] Ryan O’Donnell, Michael Saks, Oded Schramm, and Rocco A. Servedio. 2005. Every decision tree has an influential variable. In 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05). Pages 31-39. · doi:10.1109/SFCS.2005.34
[105] Ben W. Reichardt. 2011. Reflections for Quantum Query Algorithms. In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms. SODA ’11. Pages 560-569. · Zbl 1373.68230 · doi:10.1137/1.9781611973082.44
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[107] David Rubinstein. 1995. Sensitivity vs. block sensitivity of Boolean functions. Combinatorica, 15, 2, 1995. Pages 297-299. · Zbl 0837.68080 · doi:10.1007/BF01200762
[108] Michael Saks and Avi Wigderson. 1986. Probabilistic Boolean Decision Trees and the Complexity of Evaluating Game Trees. In Proceedings of the 27th Annual Symposium on Foundations of Computer Science. SFCS ’86. Pages 29-38. · doi:10.1109/SFCS.1986.44
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