skip to main content
article
Free Access

Monotone circuits for matching require linear depth

Published:01 July 1992Publication History
Skip Abstract Section

Abstract

It is proven that monotone circuits computing the perfect matching function on n-vertex graphs require Ω(n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits.

References

  1. 1 AJTAI, M., AND GUREWCn, Y. Monotone versus positive. J. A CM 34, 4 (Oct. 1987), 1004-1015. Google ScholarGoogle Scholar
  2. 2 ALON, N., AND BOPPANA, R. The monotone circuit complexity of Boolean functions. Cornbinatorica 7, 1 (1987), 1-22. Google ScholarGoogle Scholar
  3. 3 ANDREEV, A. E. On a method for obtaining lower bounds on the complexity of individual monotone functions. Dokl. Ak. Nauk. SSSR 282 (1985), 1033-1037 (in Russian). Enghsh translation in Sov. Math. Dokl. 31 (1985), 530-534.Google ScholarGoogle Scholar
  4. 4 BORODIN, A., VON ZUR GATHEN, J., AND HOPCROFT, J. Fast parallel matrix and GCD computations. In Proceedings of the 23rd Annual IEEE symposium of Foundations of Computer Science. IEEE, New York, 1982, pp. 65-71.Google ScholarGoogle Scholar
  5. 5 GOLDMANN, M., AND HASTAD, J. A lower bound for monotone clique using a communication game. Manuscript. Google ScholarGoogle Scholar
  6. 6 KALYaNASUNDAI~AM, B., A~I~ SCIqNrmER, G. The probabilistic communication complexity of set intersection. In Proceedings of the Symposium on Structure in Complexity Theory. 1987, pp. 41-49.Google ScholarGoogle Scholar
  7. 7 KARCH~aER, M. The complexity of computation and restricted machines. Ph.D dissertation. The Hebrew Univ., Jerusalem, Israel, 1988.Google ScholarGoogle Scholar
  8. 8 KARCHMER, M., AND WIGDERSON, A. Monotone circuits for connectivity reqmre super-logarithmic depth. SIAM J. Disc. Math. 3, 2 (1990), 718-727.Google ScholarGoogle Scholar
  9. 9 LOVASZ, L. Determinants, matchings and random algorithms. In L. Budach, ed., Proceedings ofFCT89. Akademie-Verlag, Berlin, 1979, pp. 565-574.Google ScholarGoogle Scholar
  10. 10 RAZ, R., AND WIGDERSON, A. Probabilistic commumcatlon complexity of Boolean relations, In Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science. IEEE, New York, 1989.Google ScholarGoogle Scholar
  11. 11 RAZBOROV, A.A. Lower bounds for the monotone complexity of some Boolean functions. Dokl. Ak. Nauk. SSSR 281 (1985), 798-801 (in Russian). English translation in Sov. Math. Dokl, 31 (1985), 354-357.Google ScholarGoogle Scholar
  12. 12 RAZBOROV, A.A. Lower bounds on the monotone network complexity of the logical permanent. Mat. Zametki 37 (1985), 887-900 (in Russian). English translation in Math. Notes of the Academy of Sciences of USSR 37 (I985), 485-493.Google ScholarGoogle Scholar
  13. 13 RAZBOROV, A. A. On the dlstnbutionaI complexity of d~sjointness In Lecture Notes in Computer Science, vol. 443. Springer-Verlag, New York, 1990, pp. 249-253. Google ScholarGoogle Scholar
  14. 14 TARDOS, E. The gap between monotone and non-monotone circmt complexity is exponennal. Combinatorica 8 (1988), 141-142.Google ScholarGoogle Scholar
  15. 15 WEGN~R, I. The Complexity of Boolean Functions. Wiley, New York, 1988.Google ScholarGoogle Scholar
  16. 16 YAo, A.C. Some complexity questions related to distributive computing. In Proceedings of the llth Annual ACM Symposium on Theory of Computing (Atlanta, Ga., Apr. 30-May 2) ACM, New York, 1979, pp. 209-213. Google ScholarGoogle Scholar

Index Terms

  1. Monotone circuits for matching require linear depth

              Recommendations

              Comments

              Login options

              Check if you have access through your login credentials or your institution to get full access on this article.

              Sign in

              Full Access

              PDF Format

              View or Download as a PDF file.

              PDF

              eReader

              View online with eReader.

              eReader