Depth lower bounds for monotone semi-unbounded fan-in circuits
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 3, pp. 277-286.

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 i1.

Classification : 68Q17, 68Q15
Mots clés : monotone circuit, semi-unbounded fan-in, communication complexity, lower bound
@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},
     pages = {277--286},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {3},
     year = {2001},
     mrnumber = {1869218},
     zbl = {1052.68053},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2001__35_3_277_0/}
}
TY  - JOUR
AU  - Johannsen, Jan
TI  - Depth lower bounds for monotone semi-unbounded fan-in circuits
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2001
SP  - 277
EP  - 286
VL  - 35
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/ITA_2001__35_3_277_0/
LA  - en
ID  - ITA_2001__35_3_277_0
ER  - 
%0 Journal Article
%A Johannsen, Jan
%T Depth lower bounds for monotone semi-unbounded fan-in circuits
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2001
%P 277-286
%V 35
%N 3
%I EDP-Sciences
%U http://www.numdam.org/item/ITA_2001__35_3_277_0/
%G en
%F 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) no. 3, pp. 277-286. http://www.numdam.org/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 | Zbl

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

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

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

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

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