Depth lower bounds for monotone semi-unbounded fan-in circuits
Johannsen, Jan
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001), p. 277-286 / Harvested from Numdam
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The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semi-unbounded fan-in. It follows that the inclusions NC i ⊆SAC i ⊆AC i are proper in the monotone setting, for every i≥1.

Publié le : 2001-01-01
Classification:  68Q17,  68Q15 
@article{ITA_2001__35_3_277_0,
     author = {Johannsen, Jan},
     title = {Depth lower bounds for monotone semi-unbounded fan-in circuits},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {35},
     year = {2001},
     pages = {277-286},
     mrnumber = {1869218},
     zbl = {1052.68053},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2001__35_3_277_0}
}

Johannsen, Jan. Depth lower bounds for monotone semi-unbounded fan-in circuits. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) pp. 277-286. http://gdmltest.u-ga.fr/item/ITA_2001__35_3_277_0/

[1] A. Borodin, S.A. Cook, P.W. Dymond, W.L. Ruzzo and M. Tompa, Two applications of inductive counting for complementation problems. SIAM J. Comput. 18 (1989) 559-578. | MR 996836 | Zbl 0678.68031

[2] M. Grigni and M. Sipser, Monotone complexity, in Boolean Function Complexity, edited by M.S. Paterson. Cambridge University Press (1992) 57-75. | MR 1211867 | Zbl 0766.68040

[3] M. Karchmer and A. Wigderson, Monotone circuits for connectivity require super-logarithmic depth. SIAM J. Discrete Math. 3 (1990) 255-265. | MR 1039296 | Zbl 0695.94021

[4] E. Kushilevitz and N. Nisan, Communication Complexity. Cambridge University Press (1997). | MR 1426129 | Zbl 0869.68048

[5] R. Raz and P. Mckenzie, Separation of the monotone NC hierarchy. Combinatorica 19 (1999) 403-435. | MR 1723255 | Zbl 0977.68037

[6] H. Venkateswaran, Properties that characterize LOGCFL. J. Comput. System Sci. 43 (1991) 380-404. | MR 1130778 | Zbl 0776.68046