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JOURNALS // Matematicheskie Zametki

Mat. Zametki, 1987, Volume 41, Issue 4, Pages 598–607 (Mi mzm4883)

Lower bounds on the size of bounded depth circuits over a complete basis with logical addition
A. A. Razborov

This publication is cited in the following articles:
  1. Josh Alman, Jingxun Liang, Proceedings of the 57th Annual ACM Symposium on Theory of Computing, 2025, 1383  crossref
  2. Lijie Chen, Ron D. Rothblum, Roei Tell, Proceedings of the 57th Annual ACM Symposium on Theory of Computing, 2025, 977  crossref
  3. Yizhi Huang, Rahul Ilango, Hanlin Ren, “NP-Hardness of Approximating Meta-Complexity: A Cryptographic Approach”, SIAM J. Comput., 54:4 (2025), 819  crossref
  4. Yuyu Wang, Lecture Notes in Computer Science, 16004, Advances in Cryptology – CRYPTO 2025, 2025, 38  crossref
  5. I. S. Sergeev, “Nizhnie otsenki additivnoi slozhnosti lineinykh operatorov i bilineinykh algoritmov umnozheniya matrits i mnogochlenov nad $GF(2)$”, Matem. zametki, 118:4 (2025), 607–624  mathnet  crossref
  6. Lijie Chen, “Nondeterministic Quasi-Polynomial Time is Average-Case Hard for \(\textsf{ACC}\) Circuits”, SIAM J. Comput., 2024, FOCS19-332  crossref
  7. Yilei Chen, Jiatu Li, Proceedings of the 56th Annual ACM Symposium on Theory of Computing, 2024, 620  crossref
  8. Shivam Nadimpalli, Natalie Parham, Francisca Vasconcelos, Henry Yuen, Proceedings of the 56th Annual ACM Symposium on Theory of Computing, 2024, 1498  crossref
  9. Yuyu Wang, Chuanjie Su, Jiaxin Pan, Lecture Notes in Computer Science, 14921, Advances in Cryptology – CRYPTO 2024, 2024, 251  crossref
  10. Ján Pich, “Localizability of the approximation method”, comput. complex., 33:2 (2024)  crossref
  11. Libor Caha, Xavier Coiteux-Roy, Robert Koenig, “Single-qubit gate teleportation provides a quantum advantage”, Quantum, 8 (2024), 1548  crossref
  12. Pooya Hatami, William M. Hoza, Avishay Tal, Roei Tell, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, 2023, 895  crossref
  13. Ronen Shaltiel, “Is it possible to improve Yao's XOR lemma using reductions that exploit the efficiency of their oracle?”, comput. complex., 32:1 (2023)  crossref
  14. Yeyuan Chen, Yizhi Huang, Jiatu Li, Hanlin Ren, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, 2023, 1058  crossref
  15. Rahul Ilango, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023, 733  crossref
  16. Yuyu Wang, Jiaxin Pan, Yu Chen, “Fine-Grained Secure Attribute-Based Encryption”, J Cryptol, 36:4 (2023)  crossref
  17. Uma Girish, Makrand Sinha, Avishay Tal, Kewen Wu, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023, 721  crossref
  18. Emmanuel Abbe, Colin Sandon, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023, 177  crossref
  19. Mika Göös, Artur Riazanov, Anastasia Sofronova, Dmitry Sokolov, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023, 1048  crossref
  20. Yizhi Huang, Rahul Ilango, Hanlin Ren, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, 2023, 1067  crossref
  21. Lijie Chen, Ce Jin, Rahul Santhanam, R. Ryan Williams, 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), 2022, 646  crossref
  22. Mark Braverman, Sumegha Garg, Or Zamir, 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), 2022, 1068  crossref
  23. Yuyu Wang, Jiaxin Pan, Lecture Notes in Computer Science, 13276, Advances in Cryptology – EUROCRYPT 2022, 2022, 305  crossref
  24. Lijie Chen, Hanlin Ren, “Strong Average-Case Circuit Lower Bounds from Nontrivial Derandomization”, SIAM J. Comput., 51:3 (2022), STOC20-115  crossref
  25. Jiatu Li, Tianqi Yang, Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, 2022, 1180  crossref
  26. Benjamin Lovitz, Vincent Steffan, “New techniques for bounding stabilizer rank”, Quantum, 6 (2022), 692  crossref
  27. Shir Peleg, Amir Shpilka, Ben Lee Volk, “Lower Bounds on Stabilizer Rank”, Quantum, 6 (2022), 652  crossref
  28. Yuyu Wang, Jiaxin Pan, Yu Chen, Lecture Notes in Computer Science, 12828, Advances in Cryptology – CRYPTO 2021, 2021, 179  crossref
  29. Xuangui Huang, Emanuele Viola, Lecture Notes in Computer Science, 12730, Computer Science – Theory and Applications, 2021, 186  crossref
  30. Itai Dinur, Lecture Notes in Computer Science, 12696, Advances in Cryptology – EUROCRYPT 2021, 2021, 374  crossref
  31. Janio Carlos Nascimento Silva, Uéverton S. Souza, Luiz Satoru Ochi, Lecture Notes in Computer Science, 13153, Algorithmic Aspects in Information and Management, 2021, 380  crossref
  32. R. Ryan Williams, “From Circuit Complexity to Faster All-Pairs Shortest Paths”, SIAM Rev., 63:3 (2021), 559  crossref
  33. Pyung Kim, Eunji Jo, Younho Lee, “An Efficient Search Algorithm for Large Encrypted Data by Homomorphic Encryption”, Electronics, 10:4 (2021), 484  crossref
  34. Mark Bun, Robin Kothari, Justin Thaler, “Quantum algorithms and approximating polynomials for composed functions with shared inputs”, Quantum, 5 (2021), 543  crossref
  35. Timothy M. Chan, R. Ryan Williams, “Deterministic APSP, Orthogonal Vectors, and More”, ACM Trans. Algorithms, 17:1 (2021), 1  crossref
  36. Daniel Grier, Luke Schaeffer, Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, 2020, 875  crossref
  37. Dmitry Sokolov, Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, 2020, 78  crossref
  38. Olaf Beyersdorff, Ilario Bonacina, Leroy Chew, Jan Pich, “Frege Systems for Quantified Boolean Logic”, J. ACM, 67:2 (2020), 1  crossref
  39. Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan, Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, 2020, 209  crossref
  40. Lijie Chen, Hanlin Ren, Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, 2020, 1327  crossref
  41. Oded Goldreich, Guy N. Rothblum, Lecture Notes in Computer Science, 12050, Computational Complexity and Property Testing, 2020, 326  crossref
  42. Prerona Chatterjee, Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), 2020, 870  crossref
  43. Charlotte Bonte, Ilia Iliashenko, Proceedings of the 2020 ACM SIGSAC Conference on Cloud Computing Security Workshop, 2020, 105  crossref
  44. Nikhil Balaji, Andreas Krebs, Nutan Limaye, “Skew circuits of small width”, Theoretical Computer Science, 821 (2020), 111  crossref
  45. Lijie Chen, Xin Lyu, R. Ryan Williams, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), 2020, 1  crossref
  46. Russell Impagliazzo, Sasank Mouli, Toniann Pitassi, Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, 2020, 591  crossref
  47. Srikanth Srinivasan, Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, 2020, 1349  crossref
  48. Roei Tell, “Improved Bounds for Quantified Derandomization of Constant-Depth Circuits and Polynomials”, comput. complex., 28:2 (2019), 259  crossref
  49. Prahladh Harsha, Srikanth Srinivasan, “On polynomial approximations to AC”, Random Struct Algorithms, 54:2 (2019), 289  crossref
  50. Adi Akavia, Craig Gentry, Shai Halevi, Max Leibovich, “Setup-Free Secure Search on Encrypted Data: Faster and Post-Processing Free”, Proceedings on Privacy Enhancing Technologies, 2019:3 (2019), 87  crossref
  51. Lijie Chen, Roei Tell, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 2019, 34  crossref
  52. Lijie Chen, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019, 1281  crossref
  53. Mrinal Kumar, Ramprasad Saptharishi, “The Computational Power of Depth Five Arithmetic Circuits”, SIAM J. Comput., 48:1 (2019), 144  crossref
  54. Marvin Künnemann, Daniel Moeller, Ramamohan Paturi, Stefan Schneider, “Subquadratic Algorithms for Succinct Stable Matching”, Algorithmica, 81:7 (2019), 2991  crossref
  55. G. V. Bokov, “Ot bulevykh skhem k dokazatelstvu teorem”, Intellektualnye sistemy. Teoriya i prilozheniya, 22:1 (2018), 123–130  mathnet
  56. Joan Boyar, Magnus Gausdal Find, “Multiplicative complexity of vector valued Boolean functions”, Theoretical Computer Science, 720 (2018), 36  crossref
  57. Tim Roughgarden, Sergei Vassilvitskii, Joshua R. Wang, “Shuffles and Circuits (On Lower Bounds for Modern Parallel Computation)”, J. ACM, 65:6 (2018), 1  crossref
  58. Fu Li, Iddo Tzameret, Zhengyu Wang, “Characterizing Propositional Proofs as Noncommutative Formulas”, SIAM J. Comput., 47:4 (2018), 1424  crossref
  59. Akinori Kawachi, “Circuit lower bounds from learning-theoretic approaches”, Theoretical Computer Science, 733 (2018), 83  crossref
  60. Matteo Campanelli, Rosario Gennaro, Lecture Notes in Computer Science, 11240, Theory of Cryptography, 2018, 66  crossref
  61. Dan Boneh, Yuval Ishai, Alain Passelègue, Amit Sahai, David J. Wu, Lecture Notes in Computer Science, 11240, Theory of Cryptography, 2018, 699  crossref
  62. Alman J. Williams R., “Probabilistic Rank and Matrix Rigidity”, Stoc'17: Proceedings of the 49Th Annual Acm Sigact Symposium on Theory of Computing, Annual Acm Symposium on Theory of Computing, ed. Hatami H. McKenzie P. King V., Assoc Computing Machinery, 2017, 641–652  crossref  isi
  63. Valentine Kabanets, Daniel M. Kane, Zhenjian Lu, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, 2017, 615  crossref
  64. Gil Cohen, Amir Shpilka, Avishay Tal, “On the degree of univariate polynomials over the integers”, Combinatorica, 37:3 (2017), 419  crossref
  65. Michael A. Forbes, Amir Shpilka, Ben Lee Volk, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, 2017, 653  crossref
  66. Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, Madars Virza, “Scalable Zero Knowledge Via Cycles of Elliptic Curves”, Algorithmica, 79:4 (2017), 1102  crossref
  67. Johan Håstad, Benjamin Rossman, Rocco A. Servedio, Li-Yang Tan, “An Average-Case Depth Hierarchy Theorem for Boolean Circuits”, J. ACM, 64:5 (2017), 1  crossref
  68. Olaf Beyersdorff, Ilario Bonacina, Chew Leroy, Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, 2016, 249  crossref
  69. Zachary Remscrim, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), 2016, 197  crossref
  70. Daniel Moeller, Ramamohan Paturi, Stefan Schneider, Lecture Notes in Computer Science, 9691, Computer Science – Theory and Applications, 2016, 294  crossref
  71. Josh Alman, Timothy M. Chan, Ryan Williams, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), 2016, 467  crossref
  72. Akshay Degwekar, Vinod Vaikuntanathan, Prashant Nalini Vasudevan, Lecture Notes in Computer Science, 9816, Advances in Cryptology – CRYPTO 2016, 2016, 533  crossref
  73. Emmanuel Abbe, Amir Shpilka, Avi Wigderson, Proceedings of the forty-seventh annual ACM symposium on Theory of Computing, 2015, 297  crossref
  74. Brendan Juba, Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, 2015, 93  crossref
  75. Emmanuel Abbe, Amir Shpilka, Avi Wigderson, “Reed–Muller Codes for Random Erasures and Errors”, IEEE Trans. Inform. Theory, 61:10 (2015), 5229  crossref
  76. Benjamin Rossman, Rocco A. Servedio, Li-Yang Tan, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 2015, 1030  crossref
  77. Benjamin Rossman, Rocco A. Servedio, Li-Yang Tan, “Complexity Theory Column 89”, SIGACT News, 46:4 (2015), 50  crossref
  78. Joan Boyar, Magnus Gausdal Find, Lecture Notes in Computer Science, 9210, Fundamentals of Computation Theory, 2015, 106  crossref
  79. Joshua A. Grochow, “Unifying Known Lower Bounds via Geometric Complexity Theory”, comput. complex., 24:2 (2015), 393  crossref
  80. Chia-Jung Lee, Satyanarayana V. Lokam, Shi-Chun Tsai, Ming-Chuan Yang, 2015 IEEE International Symposium on Information Theory (ISIT), 2015, 501  crossref
  81. Josh Alman, Ryan Williams, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 2015, 136  crossref
  82. Ruiwen Chen, Valentine Kabanets, Antonina Kolokolova, Ronen Shaltiel, David Zuckerman, “Mining Circuit Lower Bound Proofs for Meta-Algorithms”, comput. complex., 24:2 (2015), 333  crossref
  83. Hervé Fournier, Nutan Limaye, Meena Mahajan, Srikanth Srinivasan, Lecture Notes in Computer Science, 9235, Mathematical Foundations of Computer Science 2015, 2015, 324  crossref
  84. Nikhil Balaji, Andreas Krebs, Nutan Limaye, Lecture Notes in Computer Science, 9198, Computing and Combinatorics, 2015, 199  crossref
  85. Andrew Drucker, Fabian Kuhn, Rotem Oshman, Proceedings of the 2014 ACM symposium on Principles of distributed computing, 2014, 367  crossref
  86. Akinori KAWACHI, “Proving Circuit Lower Bounds in High Uniform Classes”, IIS, 20:1 (2014), 1  crossref
  87. Ryan Williams, 2014 IEEE 29th Conference on Computational Complexity (CCC), 2014, 248  crossref
  88. Ruiwen Chen, Valentine Kabanets, Antonina Kolokolova, Ronen Shaltiel, David Zuckerman, 2014 IEEE 29th Conference on Computational Complexity (CCC), 2014, 262  crossref
  89. Ryan Williams, Proceedings of the forty-sixth annual ACM symposium on Theory of computing, 2014, 664  crossref
  90. Kei UCHIZAWA, “Lower Bounds for Threshold Circuits of Bounded Energy”, IIS, 20:1 (2014), 27  crossref
  91. Kristoffer Arnsfelt Hansen, Balagopal Komarath, Jayalal Sarma, Sven Skyum, Navid Talebanfard, Lecture Notes in Computer Science, 8635, Mathematical Foundations of Computer Science 2014, 2014, 336  crossref
  92. Albert Atserias, Anuj Dawar, “Degree lower bounds of tower-type for approximating formulas with parity quantifiers”, ACM Trans. Comput. Logic, 15:1 (2014), 1  crossref
  93. Ruiwen Chen, Valentine Kabanets, Jeff Kinne, “Lower Bounds Against Weakly-Uniform Threshold Circuits”, Algorithmica, 70:1 (2014), 47  crossref
  94. Arkadev Chattopadhyay, Ricard Gavaldà, Kristoffer Arnsfelt Hansen, Denis Thérien, “Learning Read-Constant Polynomials of Constant Degree Modulo Composites”, Theory Comput Syst, 55:2 (2014), 404  crossref
  95. Benjamin Rossman, Proceedings of the forty-sixth annual ACM symposium on Theory of computing, 2014, 203  crossref
  96. Ryan Williams, “Nonuniform ACC Circuit Lower Bounds”, J. ACM, 61:1 (2014), 1  crossref
  97. Alexander A. Razborov, The Mathematics of Paul Erdős I, 2013, 425  crossref
  98. Andrej Bogdanov, Akinori Kawachi, Hidetoki Tanaka, “Hard Functions for Low-Degree Polynomials over Prime Fields”, ACM Trans. Comput. Theory, 5:2 (2013), 1  crossref
  99. Shachar Lovett, Partha Mukhopadhyay, Amir Shpilka, “Pseudorandom generators for CC0[p] and the Fourier spectrum of low-degree polynomials over finite fields”, comput. complex., 22:4 (2013), 679  crossref
  100. Arkadev Chattopadhyay, Jacobo Torán, Fabian Wagner, “Graph Isomorphism is Not AC0-Reducible to Group Isomorphism”, ACM Trans. Comput. Theory, 5:4 (2013), 1  crossref
  101. A. P. Davydow, S. I. Nikolenko, “Circuit complexity of linear functions: gate elimination and feeble security”, J. Math. Sci. (N. Y.), 188:1 (2013), 35–46  mathnet  crossref  mathscinet
  102. Ruiwen Chen, Valentine Kabanets, Lecture Notes in Computer Science, 7434, Computing and Combinatorics, 2012, 408  crossref
  103. V. V. Podolskii, “Exponential lower bound for bounded depth circuits with few threshold gates”, Inform. Process. Lett., 112:7 (2012), 267–271  mathnet  crossref  isi  scopus
  104. Guy N. Rothblum, Lecture Notes in Computer Science, 7417, Advances in Cryptology – CRYPTO 2012, 2012, 552  crossref
  105. Albert Atserias, Anuj Dawar, Lecture Notes in Computer Science, 7392, Automata, Languages, and Programming, 2012, 67  crossref
  106. Dmitry Gavinsky, Shachar Lovett, Srikanth Srinivasan, 2012 IEEE 27th Conference on Computational Complexity, 2012, 287  crossref
  107. Ido Ben-Eliezer, Rani Hod, Shachar Lovett, “Random low-degree polynomials are hard to approximate”, comput. complex., 21:1 (2012), 63  crossref
  108. Gil Cohen, Amir Shpilka, Avishay Tal, Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, 2012, 409  crossref
  109. Richard J. Lipton, Kenneth W. Regan, Atri Rudra, Lecture Notes in Computer Science, 6907, Mathematical Foundations of Computer Science 2011, 2011, 436  crossref
  110. Andrej Bogdanov, Akinori Kawachi, Hidetoki Tanaka, Lecture Notes in Computer Science, 6907, Mathematical Foundations of Computer Science 2011, 2011, 120  crossref
  111. Arkadev Chattopadhyay, Ricard Gavaldà, Kristoffer Arnsfelt Hansen, Denis Thérien, Lecture Notes in Computer Science, 6651, Computer Science – Theory and Applications, 2011, 29  crossref
  112. Fengming Wang, Lecture Notes in Computer Science, 6648, Theory and Applications of Models of Computation, 2011, 164  crossref
  113. Arkadev Chattopadhyay, Shachar Lovett, 2011 IEEE 26th Annual Conference on Computational Complexity, 2011, 300  crossref
  114. Sebastian Faust, Tal Rabin, Leonid Reyzin, Eran Tromer, Vinod Vaikuntanathan, Lecture Notes in Computer Science, 6110, Advances in Cryptology – EUROCRYPT 2010, 2010, 135  crossref
  115. Mark Braverman, “Polylogarithmic independence fools AC 0 circuits”, J. ACM, 57:5 (2010), 1  crossref
  116. Parikshit Gopalan, Subhash Khot, Rishi Saket, “Hardness of Reconstructing Multivariate Polynomials over Finite Fields”, SIAM J. Comput., 39:6 (2010), 2598  crossref
  117. Shachar Lovett, Partha Mukhopadhyay, Amir Shpilka, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, 2010, 695  crossref
  118. Omer Barkol, Yuval Ishai, Enav Weinreb, “On d-Multiplicative Secret Sharing”, J Cryptol, 23:4 (2010), 580  crossref
  119. Mark Braverman, 2009 24th Annual IEEE Conference on Computational Complexity, 2009, 3  crossref
  120. Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky, Amit Sahai, “Zero-Knowledge Proofs from Secure Multiparty Computation”, SIAM J. Comput., 39:3 (2009), 1121  crossref
  121. Parikshit Gopalan, Shachar Lovett, Amir Shpilka, 2009 24th Annual IEEE Conference on Computational Complexity, 2009, 173  crossref
  122. Rahul Santhanam, “Circuit Lower Bounds for Merlin–Arthur Classes”, SIAM J. Comput., 39:3 (2009), 1038  crossref
  123. Benjamin Rossman, Lecture Notes in Computer Science, 5514, Logic, Language, Information and Computation, 2009, 350  crossref
  124. Arkadev Chattopadhyay, Avi Wigderson, 2009 50th Annual IEEE Symposium on Foundations of Computer Science, 2009, 43  crossref
  125. Ido Ben-Eliezer, Rani Hod, Shachar Lovett, Lecture Notes in Computer Science, 5687, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 2009, 366  crossref
  126. Kristoffer Arnsfelt Hansen, Lecture Notes in Computer Science, 5675, Computer Science - Theory and Applications, 2009, 117  crossref
  127. Kristoffer Arnsfelt Hansen, Michal Koucký, 2009 24th Annual IEEE Conference on Computational Complexity, 2009, 27  crossref
  128. Vladimir V. Podolskii, Lecture Notes in Computer Science, 5010, Computer Science – Theory and Applications, 2008, 261  crossref
  129. Yael Tauman Kalai, Ran Raz, Lecture Notes in Computer Science, 5126, Automata, Languages and Programming, 2008, 536  crossref
  130. Parikshit Gopalan, “Query-Efficient Algorithms for Polynomial Interpolation over Composites”, SIAM J. Comput., 38:3 (2008), 1033  crossref
  131. Pavel Pudlák, Lecture Notes in Computer Science, 5010, Computer Science – Theory and Applications, 2008, 13  crossref
  132. Omer Barkol, Yuval Ishai, Enav Weinreb, Proceedings of the fortieth annual ACM symposium on Theory of computing, 2008, 661  crossref
  133. Kristoffer Arnsfelt Hansen, 2008 23rd Annual IEEE Conference on Computational Complexity, 2008, 92  crossref
  134. Ran Raz, Amir Yehudayoff, 2008 23rd Annual IEEE Conference on Computational Complexity, 2008, 128  crossref
  135. Rahul Santhanam, Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, 2007, 275  crossref
  136. Debajyoti Bera, Frederic Green, Steven Homer, “Small depth quantum circuits”, SIGACT News, 38:2 (2007), 35  crossref
  137. Parikshit Gopalan, Subhash Khot, Rishi Saket, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), 2007, 349  crossref
  138. Amitabha Roy, Howard Straubing, “Definability of Languages by Generalized First-Order Formulas over $(\mathbb{N},+)$”, SIAM J. Comput., 37:2 (2007), 502  crossref
  139. Alexander Healy, Emanuele Viola, Lecture Notes in Computer Science, 3884, STACS 2006, 2006, 672  crossref
  140. J. Buresh-Oppenheim, R. Santhanam, 21st Annual IEEE Conference on Computational Complexity (CCC'06), 2006, 73  crossref
  141. Nayantara Bhatnagar, Parikshit Gopalan, Richard J. Lipton, “Symmetric polynomials over Zm and simultaneous communication protocols”, Journal of Computer and System Sciences, 72:2 (2006), 252  crossref
  142. Amitabha Roy, Howard Straubing, Lecture Notes in Computer Science, 3884, STACS 2006, 2006, 489  crossref
  143. Lane A. Hemaspaandra, “SIGACT news complexity theory column 53”, SIGACT News, 37:4 (2006), 47  crossref
  144. Arkadev Chattopadhyay, Kristoffer Arnsfelt Hansen, Lecture Notes in Computer Science, 3580, Automata, Languages and Programming, 2005, 994  crossref
  145. Stephen Fenner, Frederic Green, Steven Homer, Yong Zhang, Lecture Notes in Computer Science, 3623, Fundamentals of Computation Theory, 2005, 44  crossref
  146. Omer Barkol, Yuval Ishai, Lecture Notes in Computer Science, 3621, Advances in Cryptology – CRYPTO 2005, 2005, 395  crossref
  147. Farid Ablayev, Aida Gainutdinova, Marek Karpinski, Cristopher Moore, Christopher Pollett, “On the computational power of probabilistic and quantum branching program”, Information and Computation, 203:2 (2005), 145  crossref
  148. Jin-Yi Cai, Osamu Watanabe, Lecture Notes in Computer Science, 3341, Algorithms and Computation, 2004, 209  crossref
  149. A. D. Korshunov, “Monotone Boolean functions”, Russian Math. Surveys, 58:5 (2003), 929–1001  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  150. Peter Høyer, Robert Špalek, Lecture Notes in Computer Science, 2607, STACS 2003, 2003, 234  crossref
  151. Ran Raz, Amir Shpilka, “Lower Bounds for Matrix Product in Bounded Depth Circuits with Arbitrary Gates”, SIAM J. Comput., 32:2 (2003), 488  crossref
  152. V. Beiu, 2, Proceedings of the International Joint Conference on Neural Networks, 2003., 2003, 989  crossref
  153. Adam R. Klivans, Lecture Notes in Computer Science, 2129, Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques, 2001, 249  crossref
  154. Cristopher Moore, Denis Thérien, François Lemieux, Joshua Berman, Arthur Drisko, “Circuits and Expressions with Nonassociative Gates”, Journal of Computer and System Sciences, 60:2 (2000), 368  crossref
  155. Y. Ishai, E. Kushilevitz, Proceedings 41st Annual Symposium on Foundations of Computer Science, 2000, 294  crossref
  156. Carsten Damm, Ki Hang Kim, Fred Roush, Lecture Notes in Computer Science, 1627, Computing and Combinatorics, 1999, 123  crossref
  157. Howard Straubing, Lecture Notes in Computer Science, 1373, STACS 98, 1998, 332  crossref
  158. D. Grigoriev, A.A. Razborov, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280), 1998, 269  crossref
  159. Uwe Schöning, Randall Pruim, Gems of Theoretical Computer Science, 1998, 101  crossref
  160. Alexis Maciel, Denis Thérien, “Threshold Circuits of Small Majority-Depth”, Information and Computation, 146:1 (1998), 55  crossref
  161. Cristopher Moore, “Predicting nonlinear cellular automata quickly by decomposing them into linear ones”, Physica D: Nonlinear Phenomena, 111:1-4 (1998), 27  crossref
  162. Mikael Goldmann, Johan Håstad, “Monotone Circuits for Connectivity Have Depth (log n)2-o(1)”, SIAM J. Comput., 27:5 (1998), 1283  crossref
  163. R. Paturi, P. Pudlak, F. Zane, Proceedings 38th Annual Symposium on Foundations of Computer Science, 1997, 566  crossref
  164. Alexander A Razborov, Steven Rudich, “Natural Proofs”, Journal of Computer and System Sciences, 55:1 (1997), 24  crossref
  165. Domenico Zambella, “Algebraic Methods and Bounded Formulas”, Notre Dame J. Formal Logic, 38:1 (1997)  crossref
  166. M. Agrawal, E. Allender, S. Datta, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference, 1997, 134  crossref
  167. R. Beigel, A. Maciel, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference, 1997, 149  crossref
  168. Pierre Péladeau, Howard Straubing, Denis Therien, “Finite semigroup varieties defined by programs”, Theoretical Computer Science, 180:1-2 (1997), 325  crossref
  169. Shi-Chun Tsai, “Lower Bounds on Representing Boolean Functions as Polynomials in $Z_m $”, SIAM J. Discrete Math., 9:1 (1996), 55  crossref
  170. Jordan Gergov, Christoph Meinel, “Mod-2-OBDDs—A data structure that generalizes EXOR-sum-of-products and ordered binary decision diagrams”, Form Method Syst Des, 8:3 (1996), 273  crossref
  171. Hervé Caussinus, “A note on a theorem of Barrington, Straubing and Thérien”, Information Processing Letters, 58:1 (1996), 31  crossref
  172. Jehoshua Bruck, “Reflections on ?Representations of sets of Boolean functions by commutative rings? by Roman Smolensky”, Comput Complexity, 6:3 (1996), 209  crossref
  173. Richard Beigel, Alexis Maciel, “Upper and lower bounds for some depth-3 circuit classes”, Comput Complexity, 6:3 (1996), 235  crossref
  174. Iain A. Stewart, Collegium Logicum, 2, Collegium Logicum, 1996, 101  crossref
  175. E. N. Mayoraz, “On the Power of Democratic Networks”, SIAM J. Discrete Math., 9:2 (1996), 258  crossref
  176. Eric Allender, Lecture Notes in Computer Science, 1090, Computing and Combinatorics, 1996, 127  crossref
  177. Izv. Math., 59:1 (1995), 205–227  mathnet  crossref  mathscinet  zmath  isi
  178. G. Tardos, D.A.M. Barrington, Proceedings Third Israel Symposium on the Theory of Computing and Systems, 1995, 52  crossref
  179. J. H�stad, S. Jukna, P. Pudl�k, “Top-down lower bounds for depth-three circuits”, Comput Complexity, 5:2 (1995), 99  crossref
  180. Meera Sitharam, “Evaluating spectral norms for constant depth circuits with symmetric gates”, Comput Complexity, 5:2 (1995), 167  crossref
  181. A. Gal, Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference, 1995, 82  crossref
  182. Alexander A. Razborov, Feasible Mathematics II, 1995, 344  crossref
  183. J. Kobler, Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference, 1995, 246  crossref
  184. Mikael Goldmann, “A note on the power of majority gates and modular gates”, Information Processing Letters, 53:6 (1995), 321  crossref
  185. V.P. Roychowdhury, A. Orlitsky, Kai-Yeung Siu, “Lower bounds on threshold and related circuits via communication complexity”, IEEE Trans. Inform. Theory, 40:2 (1994), 467  crossref
  186. Eric Allender, Vivek Gore, “A Uniform Circuit Lower Bound for the Permanent”, SIAM J. Comput., 23:5 (1994), 1026  crossref
  187. J. Aspnes, R. Beigel, M. Furst, S. Rudich, “The expressive power of voting polynomials”, Combinatorica, 14:2 (1994), 135  crossref
  188. Lance Fortnow, Lecture Notes in Computer Science, 880, Foundation of Software Technology and Theoretical Computer Science, 1994, 256  crossref
  189. Noam Nisan, Mario Szegedy, “On the degree of boolean functions as real polynomials”, Comput Complexity, 4:4 (1994), 301  crossref
  190. Richard Beigel, Jun Tarui, “On ACC”, Comput Complexity, 4:4 (1994), 350  crossref
  191. David A. Mix Barrington, Richard Beigel, Steven Rudich, “Representing Boolean functions as polynomials modulo composite numbers”, Comput Complexity, 4:4 (1994), 367  crossref
  192. P. Pudlák, Lecture Notes in Computer Science, 710, Fundamentals of Computation Theory, 1993, 106  crossref
  193. M. Karchmer, A. Wigderson, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference, 1993, 102  crossref
  194. Mario Szegedy, “Functions with bounded symmetric communication complexity, programs over commutative monoids, and ACC”, Journal of Computer and System Sciences, 47:3 (1993), 405  crossref
  195. Rafi Heiman, Ilan Newman, Avi Wigderson, “On read-once threshold formulae and their randomized decision tree complexity”, Theoretical Computer Science, 107:1 (1993), 63  crossref
  196. S.-C. Tsai, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference, 1993, 96  crossref
  197. R. Smolensky, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science, 1993, 130  crossref
  198. R. Beigel, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference, 1993, 82  crossref
  199. Carl Sturtivant, Gudmund Skovbjerg Frandsen, “The computational efficacy of finite-field arithmetic”, Theoretical Computer Science, 112:2 (1993), 291  crossref
  200. J. Hastad, S. Jukna, P. Pudlak, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science, 1993, 124  crossref
  201. Jehoshua Bruck, Roman Smolensky, “Polynomial Threshold Functions, $AC^0 $ Functions, and Spectral Norms”, SIAM J. Comput., 21:1 (1992), 33  crossref
  202. Joan Boyar, Gudmund Frandsen, Carl Sturtivant, “An arithmetic model of computation equivalent to threshold circuits”, Theoretical Computer Science, 93:2 (1992), 303  crossref
  203. D.A.M. Barrington, [1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference, 1992, 86  crossref
  204. David A. Mix Barrington, Kevin Compton, Howard Straubing, Denis Thérien, “Regular languages in NC1”, Journal of Computer and System Sciences, 44:3 (1992), 478  crossref
  205. Richard Beigel, Jun Tarui, Seinosuke Toda, Lecture Notes in Computer Science, 650, Algorithms and Computation, 1992, 420  crossref
  206. Mikael Goldmann, Johan Håstad, “A simple lower bound for monotone clique using a communication game”, Information Processing Letters, 41:4 (1992), 221  crossref
  207. Carsten Damm, Matthias Krause, Christoph Meinel, Stephan Waack, Lecture Notes in Computer Science, 577, STACS 92, 1992, 279  crossref
  208. I. E. Shparlinski, “On some problems in the theory of finite fields”, Russian Math. Surveys, 46:1 (1991), 199–240  mathnet  crossref  mathscinet  zmath  adsnasa
  209. R. Beigel, N. Reingold, D. Spielman, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference, 1991, 286  crossref
  210. R. Beigel, J. Tarui, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science, 1991, 783  crossref
  211. Jeff Kahn, Roy Meshulam, “On modp transversals”, Combinatorica, 11:1 (1991), 17  crossref
  212. Eddy Mayoraz, Lecture Notes in Computer Science, 540, Artificial Neural Networks, 1991, 78  crossref
  213. Jun Tarui, Lecture Notes in Computer Science, 480, STACS 91, 1991, 238  crossref
  214. David A. Mix Barrington, James Corbett, “A note on some languages in uniform ACC0”, Theoretical Computer Science, 78:2 (1991), 357  crossref
  215. R. Smolensky, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, 1990, 628  crossref
  216. Eric Allender, Ulrich Hertrampf, Lecture Notes in Computer Science, 452, Mathematical Foundations of Computer Science 1990, 1990, 158  crossref
  217. Ravi B. BOPPANA, Michael SIPSER, Algorithms and Complexity, 1990, 757  crossref
  218. David A. Mix Barrington, Neil Immerman, Howard Straubing, “On uniformity within NC1”, Journal of Computer and System Sciences, 41:3 (1990), 274  crossref
  219. J. Bruck, R. Smolensky, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, 1990, 632  crossref
  220. Jin-yi Cai, “Lower bounds for constant-depth circuits in the presence of help bits”, Information Processing Letters, 36:2 (1990), 79  crossref
  221. R. Heiman, I. Newman, A. Wigderson, Proceedings Fifth Annual Structure in Complexity Theory Conference, 1990, 78  crossref
  222. Jehoshua Bruck, “Harmonic Analysis of Polynomial Threshold Functions”, SIAM J. Discrete Math., 3:2 (1990), 168  crossref
  223. David A. Mix Barrington, James Corbett, “On the relative complexity of some languages in NC1”, Information Processing Letters, 32:5 (1989), 251  crossref
  224. J.-Y. Cai, 30th Annual Symposium on Foundations of Computer Science, 1989, 532  crossref


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