TC0 (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "TC0" in English language version.

refsWebsite

Global rank English rank

27doi.org

2^nd place

12worldcat.org

5^th place

5springer.com

274^th place

309^th place

3elsevier.com

610^th place

704^th place

3ieee.org

652^nd place

515^th place

3acm.org

1,185^th place

840^th place

1books.google.com

3^rd place

1zbmath.org

1,923^rd place

1,068^th place

1nsf.gov

3,828^th place

2,823^rd place

1handle.net

102^nd place

76^th place

1uchicago.edu

230^th place

214^th place

1weizmann.ac.il

4,983^rd place

8,002^nd place

1arxiv.org

69^th place

59^th place

1siam.org

low place

6,473^rd place

1mit.edu

415^th place

327^th place

1nih.gov

4^th place

1sciencedirect.com

149^th place

178^th place

1archive.org

6^th place

1ams.org

451^st place

277^th place

acm.org

dl.acm.org

Naor, Moni; Reingold, Omer (March 2004). "Number-theoretic constructions of efficient pseudo-random functions". Journal of the ACM. 51 (2): 231–262. doi:10.1145/972639.972643. ISSN 0004-5411.
Allender, Eric; Koucký, Michal (March 2010). "Amplifying lower bounds by means of self-reducibility". Journal of the ACM. 57 (3): 1–36. doi:10.1145/1706591.1706594. ISSN 0004-5411.

portal.acm.org

Ajtai, Miklos; Ben-Or, Michael (1984). "A theorem on probabilistic constant depth Computations". Proceedings of the sixteenth annual ACM symposium on Theory of computing - STOC '84. ACM Press. pp. 471–474. doi:10.1145/800057.808715. ISBN 978-0-89791-133-7.

ams.org

mathscinet.ams.org

Sherstov, Alexander A. (2009), "Separating $AC 0$ from depth-2 majority circuits", SIAM Journal on Computing, 38 (6): 2113–2129, doi:10.1137/08071421X, MR 2491551

archive.org

scholar.archive.org

Yao, Andrew Chi-Chih (1990). "On ACC and threshold circuits". 31st Annual Symposium on Foundations of Computer Science, St. Louis, Missouri, USA, October 22–24, 1990, Volume II. IEEE Computer Society. pp. 619–627. doi:10.1109/FSCS.1990.89583. ISBN 0-8186-2082-X.

arxiv.org

Volkov, Sergey. (2016). "Finite Bases with Respect to the Superposition in Classes of Elementary Recursive Functions, dissertation". arXiv:1611.04843 [cs.CC].

books.google.com

Vollmer, Heribert (1998). Introduction to circuit complexity. A uniform approach. Texts in Theoretical Computer Science. Berlin: Springer-Verlag. p. 126. ISBN 3-540-64310-9. Zbl 0931.68055.

doi.org

Hesse, William; Allender, Eric; Mix Barrington, David (2002). "Uniform constant-depth threshold circuits for division and iterated multiplication". Journal of Computer and System Sciences. 65 (4): 695–716. doi:10.1016/S0022-0000(02)00025-9.
Parberry, Ian; Schnitger, Georg (1988-06-01). "Parallel computation with threshold functions". Journal of Computer and System Sciences. 36 (3): 278–302. doi:10.1016/0022-0000(88)90030-X. ISSN 0022-0000.
Agrawal, Manindra; Allender, Eric; Datta, Samir (April 2000). "On TC0, AC0, and Arithmetic Circuits". Journal of Computer and System Sciences. 60 (2): 395–421. doi:10.1006/jcss.1999.1675.
Naor, Moni; Reingold, Omer (March 2004). "Number-theoretic constructions of efficient pseudo-random functions". Journal of the ACM. 51 (2): 231–262. doi:10.1145/972639.972643. ISSN 0004-5411.
Hatami, Pooya; Hoza, William M.; Tal, Avishay; Tell, Roei (February 2022). "Fooling Constant-Depth Threshold Circuits (Extended Abstract)". 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS). IEEE. pp. 104–115. doi:10.1109/FOCS52979.2021.00019. ISBN 978-1-6654-2055-6.
Williams, Ryan (June 2011). "Non-uniform ACC Circuit Lower Bounds". 2011 IEEE 26th Annual Conference on Computational Complexity. pp. 115–125. doi:10.1109/CCC.2011.36. ISBN 978-1-4577-0179-5.
Allender, Eric; Koucký, Michal (March 2010). "Amplifying lower bounds by means of self-reducibility". Journal of the ACM. 57 (3): 1–36. doi:10.1145/1706591.1706594. ISSN 0004-5411.
Mix Barrington, David A.; Immerman, Neil; Straubing, Howard (1990-12-01). "On uniformity within NC1". Journal of Computer and System Sciences. 41 (3): 274–306. doi:10.1016/0022-0000(90)90022-D. ISSN 0022-0000.
Hesse, William (2001), Orejas, Fernando; Spirakis, Paul G.; van Leeuwen, Jan (eds.), "Division Is In Uniform TC0", Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 2076, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 104–114, doi:10.1007/3-540-48224-5_9, ISBN 978-3-540-42287-7, retrieved 2025-03-19
Santhanam, Rahul; Williams, Ryan (2014-06-01). "On Uniformity and Circuit Lower Bounds". Computational Complexity. 23 (2): 177–205. doi:10.1007/s00037-014-0087-y. hdl:20.500.11820/d254202f-5539-45ba-ba25-cfe680aa46e9. ISSN 1420-8954.
Allender, Eric (1999). "The permanent requires large uniform threshold circuits". Chicago Journal of Theoretical Computer Science. 5 (1): 1–19. doi:10.4086/cjtcs.1999.007. ISSN 1073-0486.
Allender, E. (1996). "A note on uniform circuit lower bounds for the counting hierarchy". Proceedings 2nd International Computing and Combinatorics Conference (COCOON). Springer Lecture Notes in Computer Science. Vol. 1090. pp. 127–135. As cited in Burtschick, Hans-Jörg; Vollmer, Heribert (1998). "Lindström quantifiers and leaf language definability". International Journal of Foundations of Computer Science. 9 (3): 277–294. doi:10.1142/S0129054198000180. ECCC TR96-005.
Goldmann, Mikael; Håstad, Johan; Razborov, Alexander (1992-12-01). "Majority gates vs. general weighted threshold gates". Computational Complexity. 2 (4): 277–300. doi:10.1007/BF01200426. ISSN 1420-8954.
Goldmann, Mikael; Karpinski, Marek (February 1998). "Simulating Threshold Circuits by Majority Circuits". SIAM Journal on Computing. 27 (1): 230–246. doi:10.1137/S0097539794274519. ISSN 0097-5397.
Alon, Noga; Vũ, Văn H (1997-07-01). "Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs". Journal of Combinatorial Theory, Series A. 79 (1): 133–160. doi:10.1006/jcta.1997.2780. ISSN 0097-3165.
Šíma, Jiří; Orponen, Pekka (2003-12-01). "General-Purpose Computation with Neural Networks: A Survey of Complexity Theoretic Results". Neural Computation. 15 (12): 2727–2778. doi:10.1162/089976603322518731. ISSN 0899-7667. PMID 14629867.
Maass, W.; Schnitger, G.; Sontag, E.D. (1991). "On the computational power of sigmoid versus Boolean threshold circuits". [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science. IEEE Comput. Soc. Press. pp. 767–776. doi:10.1109/SFCS.1991.185447. ISBN 978-0-8186-2445-2.
Hajnal, András; Maass, Wolfgang; Pudlák, Pavel; Szegedy, Márió; Turán, György (April 1993). "Threshold circuits of bounded depth". Journal of Computer and System Sciences. 46 (2): 129–154. doi:10.1016/0022-0000(93)90001-D.
Parberry, Ian; Schnitger, Georg (1989-01-01). "Relating Boltzmann machines to conventional models of computation". Neural Networks. 2 (1): 59–67. doi:10.1016/0893-6080(89)90015-4. ISSN 0893-6080.
Ajtai, Miklos; Ben-Or, Michael (1984). "A theorem on probabilistic constant depth Computations". Proceedings of the sixteenth annual ACM symposium on Theory of computing - STOC '84. ACM Press. pp. 471–474. doi:10.1145/800057.808715. ISBN 978-0-89791-133-7.
Forster, Jürgen; Krause, Matthias; Lokam, Satyanarayana V.; Mubarakzjanov, Rustam; Schmitt, Niels; Simon, Hans Ulrich (2001), Hariharan, Ramesh; Vinay, V.; Mukund, Madhavan (eds.), "Relations Between Communication Complexity, Linear Arrangements, and Computational Complexity", FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science, vol. 2245, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 171–182, doi:10.1007/3-540-45294-x_15, ISBN 978-3-540-43002-5, retrieved 2025-03-19
Håstad, Johan; Goldmann, Mikael (June 1991). "On the power of small-depth threshold circuits". Computational Complexity. 1 (2): 113–129. doi:10.1007/BF01272517. ISSN 1016-3328.
Allender, E. (October 1989). "A note on the power of threshold circuits". 30th Annual Symposium on Foundations of Computer Science. pp. 580–584. doi:10.1109/SFCS.1989.63538. ISBN 0-8186-1982-1.
Yao, Andrew Chi-Chih (1990). "On ACC and threshold circuits". 31st Annual Symposium on Foundations of Computer Science, St. Louis, Missouri, USA, October 22–24, 1990, Volume II. IEEE Computer Society. pp. 619–627. doi:10.1109/FSCS.1990.89583. ISBN 0-8186-2082-X.
Sherstov, Alexander A. (2009), "Separating $AC 0$ from depth-2 majority circuits", SIAM Journal on Computing, 38 (6): 2113–2129, doi:10.1137/08071421X, MR 2491551

dx.doi.org

Parberry, Ian; Schnitger, Georg (1988-06-01). "Parallel computation with threshold functions". Journal of Computer and System Sciences. 36 (3): 278–302. doi:10.1016/0022-0000(88)90030-X. ISSN 0022-0000.
Mix Barrington, David A.; Immerman, Neil; Straubing, Howard (1990-12-01). "On uniformity within NC1". Journal of Computer and System Sciences. 41 (3): 274–306. doi:10.1016/0022-0000(90)90022-D. ISSN 0022-0000.

elsevier.com

linkinghub.elsevier.com

Agrawal, Manindra; Allender, Eric; Datta, Samir (April 2000). "On TC0, AC0, and Arithmetic Circuits". Journal of Computer and System Sciences. 60 (2): 395–421. doi:10.1006/jcss.1999.1675.
Alon, Noga; Vũ, Văn H (1997-07-01). "Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs". Journal of Combinatorial Theory, Series A. 79 (1): 133–160. doi:10.1006/jcta.1997.2780. ISSN 0097-3165.
Hajnal, András; Maass, Wolfgang; Pudlák, Pavel; Szegedy, Márió; Turán, György (April 1993). "Threshold circuits of bounded depth". Journal of Computer and System Sciences. 46 (2): 129–154. doi:10.1016/0022-0000(93)90001-D.

handle.net

hdl.handle.net

Santhanam, Rahul; Williams, Ryan (2014-06-01). "On Uniformity and Circuit Lower Bounds". Computational Complexity. 23 (2): 177–205. doi:10.1007/s00037-014-0087-y. hdl:20.500.11820/d254202f-5539-45ba-ba25-cfe680aa46e9. ISSN 1420-8954.

ieee.org

ieeexplore.ieee.org

Williams, Ryan (June 2011). "Non-uniform ACC Circuit Lower Bounds". 2011 IEEE 26th Annual Conference on Computational Complexity. pp. 115–125. doi:10.1109/CCC.2011.36. ISBN 978-1-4577-0179-5.
Maass, W.; Schnitger, G.; Sontag, E.D. (1991). "On the computational power of sigmoid versus Boolean threshold circuits". [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science. IEEE Comput. Soc. Press. pp. 767–776. doi:10.1109/SFCS.1991.185447. ISBN 978-0-8186-2445-2.
Allender, E. (October 1989). "A note on the power of threshold circuits". 30th Annual Symposium on Foundations of Computer Science. pp. 580–584. doi:10.1109/SFCS.1989.63538. ISBN 0-8186-1982-1.

mit.edu

direct.mit.edu

Šíma, Jiří; Orponen, Pekka (2003-12-01). "General-Purpose Computation with Neural Networks: A Survey of Complexity Theoretic Results". Neural Computation. 15 (12): 2727–2778. doi:10.1162/089976603322518731. ISSN 0899-7667. PMID 14629867.

nih.gov

pubmed.ncbi.nlm.nih.gov

Šíma, Jiří; Orponen, Pekka (2003-12-01). "General-Purpose Computation with Neural Networks: A Survey of Complexity Theoretic Results". Neural Computation. 15 (12): 2727–2778. doi:10.1162/089976603322518731. ISSN 0899-7667. PMID 14629867.

nsf.gov

par.nsf.gov

Hatami, Pooya; Hoza, William M.; Tal, Avishay; Tell, Roei (February 2022). "Fooling Constant-Depth Threshold Circuits (Extended Abstract)". 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS). IEEE. pp. 104–115. doi:10.1109/FOCS52979.2021.00019. ISBN 978-1-6654-2055-6.

sciencedirect.com

Parberry, Ian; Schnitger, Georg (1989-01-01). "Relating Boltzmann machines to conventional models of computation". Neural Networks. 2 (1): 59–67. doi:10.1016/0893-6080(89)90015-4. ISSN 0893-6080.

siam.org

epubs.siam.org

Goldmann, Mikael; Karpinski, Marek (February 1998). "Simulating Threshold Circuits by Majority Circuits". SIAM Journal on Computing. 27 (1): 230–246. doi:10.1137/S0097539794274519. ISSN 0097-5397.

springer.com

link.springer.com

Hesse, William (2001), Orejas, Fernando; Spirakis, Paul G.; van Leeuwen, Jan (eds.), "Division Is In Uniform TC0", Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 2076, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 104–114, doi:10.1007/3-540-48224-5_9, ISBN 978-3-540-42287-7, retrieved 2025-03-19
Santhanam, Rahul; Williams, Ryan (2014-06-01). "On Uniformity and Circuit Lower Bounds". Computational Complexity. 23 (2): 177–205. doi:10.1007/s00037-014-0087-y. hdl:20.500.11820/d254202f-5539-45ba-ba25-cfe680aa46e9. ISSN 1420-8954.
Goldmann, Mikael; Håstad, Johan; Razborov, Alexander (1992-12-01). "Majority gates vs. general weighted threshold gates". Computational Complexity. 2 (4): 277–300. doi:10.1007/BF01200426. ISSN 1420-8954.
Forster, Jürgen; Krause, Matthias; Lokam, Satyanarayana V.; Mubarakzjanov, Rustam; Schmitt, Niels; Simon, Hans Ulrich (2001), Hariharan, Ramesh; Vinay, V.; Mukund, Madhavan (eds.), "Relations Between Communication Complexity, Linear Arrangements, and Computational Complexity", FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science, vol. 2245, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 171–182, doi:10.1007/3-540-45294-x_15, ISBN 978-3-540-43002-5, retrieved 2025-03-19
Håstad, Johan; Goldmann, Mikael (June 1991). "On the power of small-depth threshold circuits". Computational Complexity. 1 (2): 113–129. doi:10.1007/BF01272517. ISSN 1016-3328.

uchicago.edu

cjtcs.cs.uchicago.edu

Allender, Eric (1999). "The permanent requires large uniform threshold circuits". Chicago Journal of Theoretical Computer Science. 5 (1): 1–19. doi:10.4086/cjtcs.1999.007. ISSN 1073-0486.

weizmann.ac.il

eccc.weizmann.ac.il

Allender, E. (1996). "A note on uniform circuit lower bounds for the counting hierarchy". Proceedings 2nd International Computing and Combinatorics Conference (COCOON). Springer Lecture Notes in Computer Science. Vol. 1090. pp. 127–135. As cited in Burtschick, Hans-Jörg; Vollmer, Heribert (1998). "Lindström quantifiers and leaf language definability". International Journal of Foundations of Computer Science. 9 (3): 277–294. doi:10.1142/S0129054198000180. ECCC TR96-005.

worldcat.org

search.worldcat.org

Parberry, Ian; Schnitger, Georg (1988-06-01). "Parallel computation with threshold functions". Journal of Computer and System Sciences. 36 (3): 278–302. doi:10.1016/0022-0000(88)90030-X. ISSN 0022-0000.
Naor, Moni; Reingold, Omer (March 2004). "Number-theoretic constructions of efficient pseudo-random functions". Journal of the ACM. 51 (2): 231–262. doi:10.1145/972639.972643. ISSN 0004-5411.
Allender, Eric; Koucký, Michal (March 2010). "Amplifying lower bounds by means of self-reducibility". Journal of the ACM. 57 (3): 1–36. doi:10.1145/1706591.1706594. ISSN 0004-5411.
Mix Barrington, David A.; Immerman, Neil; Straubing, Howard (1990-12-01). "On uniformity within NC1". Journal of Computer and System Sciences. 41 (3): 274–306. doi:10.1016/0022-0000(90)90022-D. ISSN 0022-0000.
Santhanam, Rahul; Williams, Ryan (2014-06-01). "On Uniformity and Circuit Lower Bounds". Computational Complexity. 23 (2): 177–205. doi:10.1007/s00037-014-0087-y. hdl:20.500.11820/d254202f-5539-45ba-ba25-cfe680aa46e9. ISSN 1420-8954.
Allender, Eric (1999). "The permanent requires large uniform threshold circuits". Chicago Journal of Theoretical Computer Science. 5 (1): 1–19. doi:10.4086/cjtcs.1999.007. ISSN 1073-0486.
Goldmann, Mikael; Håstad, Johan; Razborov, Alexander (1992-12-01). "Majority gates vs. general weighted threshold gates". Computational Complexity. 2 (4): 277–300. doi:10.1007/BF01200426. ISSN 1420-8954.
Goldmann, Mikael; Karpinski, Marek (February 1998). "Simulating Threshold Circuits by Majority Circuits". SIAM Journal on Computing. 27 (1): 230–246. doi:10.1137/S0097539794274519. ISSN 0097-5397.
Alon, Noga; Vũ, Văn H (1997-07-01). "Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs". Journal of Combinatorial Theory, Series A. 79 (1): 133–160. doi:10.1006/jcta.1997.2780. ISSN 0097-3165.
Šíma, Jiří; Orponen, Pekka (2003-12-01). "General-Purpose Computation with Neural Networks: A Survey of Complexity Theoretic Results". Neural Computation. 15 (12): 2727–2778. doi:10.1162/089976603322518731. ISSN 0899-7667. PMID 14629867.
Parberry, Ian; Schnitger, Georg (1989-01-01). "Relating Boltzmann machines to conventional models of computation". Neural Networks. 2 (1): 59–67. doi:10.1016/0893-6080(89)90015-4. ISSN 0893-6080.
Håstad, Johan; Goldmann, Mikael (June 1991). "On the power of small-depth threshold circuits". Computational Complexity. 1 (2): 113–129. doi:10.1007/BF01272517. ISSN 1016-3328.

zbmath.org

Vollmer, Heribert (1998). Introduction to circuit complexity. A uniform approach. Texts in Theoretical Computer Science. Berlin: Springer-Verlag. p. 126. ISBN 3-540-64310-9. Zbl 0931.68055.