Symmetric approximation arguments for monotone lower bounds without sunflowers

Computational Complexity

Volumn 8, Issue 1, 1999, Pages 1-20

  Berg, C ^a   Ulfberg, S ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Circuit complexity; Lower bounds; Monotone circuits

Indexed keywords

EID: 0033442632     PISSN: 10163328     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000370050017     Document Type: Article

References (15)

1. NOGA ALON AND RAVI B. BOPPANA, The monotone circuit complexity of boolean functions. Combinatorica 7 (1987), 1-22.
2. KAZUYUKI AMANO AND AKIRA MARUOKA, Potential of the approximation method. In Proc. 37th Ann. IEEE Symp. Found. Comput. Sci., 1996, 431-440.
3. ALEXANDER E. ANDREEV, On a method for obtaining lower bounds for the complexity of individual monotone functions. Sov. Math. Dokl. 31 (1985), 530-534.
4. CHRISTER BERG, On Oracles and Circuits - Topics in Computational Complexity. PhD thesis, Royal Institute of Technology, KTH, Stockholm, Sweden, 1997.
5. RAVI B. BOPPANA AND MICHAEL SIPSER, The complexity of finite functions. In Handbook of theoretical computer science, ed. JAN VAN LEEUWEN, vol. A, Algorithms and complexity, 757-804. Elsevier/MIT Press, 1990.
6. RAVI B. BOPPANA AND MICHAEL SIPSER, The complexity of finite functions. In Handbook of theoretical computer science, ed. JAN VAN LEEUWEN, vol. A, Algorithms and complexity, 757-804. Elsevier/MIT Press, 1990.
7. PAUL ERDO″S AND RICHARD RADO, Intersection theorems for systems of sets. J. London Math. Soc. 35 (1960), 85-90.
8. ARMIN HAKEN, Counting bottlenecks to show monotone P ≠ NP. In Proc. 36th Ann. IEEE Symp. Found. Comput. Sci., 1995, 36-40.
9. ARMIN HAKEN AND STEPHEN COOK, An exponential lower bound for the size of monotone real circuits. Submitted to J. Comput. System Sci., 1996.
10. STASYS JUKNA, Finite limits and monotone computations over the reals. In Twelfth Annual IEEE Conference on Computational Complexity, 1997.
11. PAVEL PUDLÁK, Lower bounds for resolution and cutting planes proofs and monotone computations. J. Symbolic Logic, to appear (1997).
12. ALEXANDER A. RAZBOROV, Lower bounds on the monotone complexity of some boolean functions. Sov. Math. Dokl. 31 (1985), 354-357.
13. ALEXANDER A. RAZBOROV, On the method of approximations. In Proc. Twenty-first Ann. ACM Symp. Theor. Comput., 1989, 167-176.
14. JANOS SIMON AND SHI-CHUN TSAI, A note on the bottleneck counting argument. In Twelfth Annual IEEE Conference on Computational Complexity, 1997.
15. JÜRGEN TIEKENHEINRICH, A 4n lower bound on the monotone network complexity of a one-output boolean function. Inform. Process. Lett. 18 (1984), 201-202.