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Cited by 237Complexity and Algorithms in GraphsAdvanced Graph Theory ResearchComputability, Logic, AI Algorithms

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Threshold circuits of bounded depth

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Hajnal, András, Maass, Wolfgang, Pudlák, Pavel, Szegedy, Márió, Turán, György·1993·Journal of Computer and System Sciences
DOI 10.1016/0022-0000(93)90001-d
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Research works printed but not linked: 18

  1. Ajtai, 1984, Σ11 formulae on finite structures, Ann. Pure Appl. Logic, 24, 1, 10.1016/0168-0072(83)90038-6 · DOI
  2. Beame, 1986, Log depth circuits for division and related problems, SIAM J. Comput., 15, 994, 10.1137/0215070 · DOI
  3. Chandra, 1984, Constant depth reducibility, SIAM J. Comput., 13, 423, 10.1137/0213028 · DOI
  4. Dobrushin, 1977, Upper bound for the redundancy of self-correcting arrangements of unreliable functional elements, Problems Inform. Transmission, 13, 59
  5. Fagin, 1985, Bounded depth, polynomial size circuits for symmetric functions, Theoret. Comput. Sci., 36, 239, 10.1016/0304-3975(85)90045-3 · DOI
  6. Gurevich, 1984, A logic for constant depth circuits, Inform. and Control, 61, 65, 10.1016/S0019-9958(84)80062-5 · DOI
  7. Lupanov, 1961, Implementing the algebra of logic functions in terms of bounded depth formulas in the basis +, ∗, −, Dokl. Acad. Nauk. SSSR, 136, 5
  8. Lupanov, 1961, Implementing the algebra of logic functions in terms of bounded depth formulas in the basis +, ∗, -, Dokl. Acad. Nauk. SSSR, 136, 1041
  9. 1961, Sov. Phys. Dokl., 6, 107
  10. McColl, 1977, The depth of all Boolean functions, SIAM J. Comput., 6, 373, 10.1137/0206026 · DOI
  11. Parberry, 1986, Parallel computation with threshold functions, Vol. 223, 272
  12. Razborov, 1985, Lower bounds for the monotone complexity of some Boolean functions, Dokl. Akad. Nauk., 281, 798
  13. Razborov, 1987, Lower bounds for the size of circuits of bounded depth with basis { ∨, ⊕ }, Mat. Zametki, 41, 598
  14. Rumelhardt, 1986, Vol. 1
  15. Simon, 1983, A tight Ω(log log n) bound on the time for parallel RAM's to compute nondegenerate Boolean functions, Vol. 158, 151
  16. Skyum, 1983, A measure in which Boolean negation is exponentially powerful, Inform. Process. Lett., 17, 125, 10.1016/0020-0190(83)90051-0 · DOI
  17. Skyum, 1985, A complexity theory based on Boolean algebra, J. Assoc. Comput. Mach., 32, 484, 10.1145/3149.3158 · DOI
  18. Turán, 1984, The critical complexity of graph properties, Inform. Process. Lett., 18, 151, 10.1016/0020-0190(84)90019-X · DOI

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Metadata

Authors
Hajnal, A., Maass, W., Pudlák, P., Szegedy, M., & Turán, G.
Affiliations
  • HUN-REN Alfréd Rényi Institute of Mathematics (HU)
  • University of Illinois Chicago (US)
  • Czech Academy of Sciences (CZ)
  • University of Chicago (US)
ORCID
Venue
Journal of Computer and System Sciences
Publisher
Elsevier BV
Published
1993-04
Volume
46
Issue
2
Pages
129-154
ISSN
0022-0000 (ISSN-L)
DOI
10.1016/0022-0000(93)90001-d
OpenAlex
W2080210666
Cited by
237
References
0
Citations by year
2026: 3 · 2025: 3 · 2024: 6 · 2023: 6 · 2022: 6 · 2021: 9 · 2020: 7 · 2019: 8 · 2018: 8 · 2017: 9 · 2016: 8 · 2015: 7 · 2014: 10 · 2013: 6 · 2012: 4
FWCI
8.66
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Computer and System Sciences (publishedVersion)
  • Journal of Computer and System Sciences
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Graph Theory Research
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
Keywords
threshold circuits, bounded-depth circuits, polynomial-size circuits, parallel computing, circuit lower bounds, probabilistic circuits, threshold gates, graph connectivity, definability

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