论文信息 - A lower bound for the monotone depth of connectivity

A lower bound for the monotone depth of connectivity

We show that any monotone circuit for computing graph connectivity must have a depth greater than /spl Omega/((log n)/sup 3/2// log log n). This proves that UCONN/sub n/ is not in monotone NC/sup 1/. The proof technique, which is an adaptation of Razborov's approximation method, is also used to derive lower bounds for a general class of graph problems.<<ETX>>

Andrew Chi-Chih Yao | A. Yao

[1] P. Erdös,et al. Intersection Theorems for Systems of Sets , 1960 .

[2] Mihalis Yannakakis,et al. On monotone formulae with restricted depth , 1984, STOC '84.

[3] A. Razborov. Lower bounds on monotone complexity of the logical permanent , 1985 .

[4] Ravi B. Boppana,et al. Threshold Functions and Bounded Depth Monotone Circuits , 1986, J. Comput. Syst. Sci..

[5] Noga Alon,et al. The monotone circuit complexity of boolean functions , 1987, Comb..

[6] Andrew Chi-Chih Yao. Circuits and local computation , 1989, STOC '89.

[7] Johan Håstad,et al. On the power of small-depth threshold circuits , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[8] Alexander A. Razborov,et al. Applications of matrix methods to the theory of lower bounds in computational complexity , 1990, Comb..

[9] Avi Wigderson,et al. Monotone Circuits for Connectivity Require Super-Logarithmic Depth , 1990, SIAM J. Discret. Math..

[10] M. Sipser,et al. Monotone Separation of Logspace from NC. , 1991 .

[11] A. Wigderson,et al. Monotone circuits for matching require linear depth , 1992, JACM.

[12] Johan Håstad,et al. A Simple Lower Bound for Monotone Clique Using a Communication Game , 1992, Inf. Process. Lett..

[13] Avi Wigderson,et al. The Complexity of Graph Connectivity , 1992, MFCS.