Amplification by read-once formulas

SIAM Journal on Computing

Volumn 26, Issue 1, 1997, Pages 15-38

  Dubiner, Moshe ^a   Zwick, Uri ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Amplification; Boolean formula; Circuit complexity

Indexed keywords

EID: 5544275298     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S009753979223633X     Document Type: Article

References (19)

1. L. ADLEMAN, Two theorems on random polynomial time, in Proc. 19th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1978, pp. 75-83.
2. M. AJTAI AND M. BEN-OR, A theorem on probabilistic constant depth computations, in Proc. 16th Annual ACM Symposium on Theory of Computing, ACM, New York, 1984, pp. 471-474.
3. A with probability 1, SIAM J. Comput., 10 (1981), pp. 96-113.
4. R. BOPPANA, Amplification of probabilistic Boolean formulas, in Advances in Computer Research, Vol. 5: Randomness and Computation, JAI Press, Greenwich, CI, 1989, pp. 27-45.
5. M. DUBINER AND U. ZWICK. Amplification and percolation, in Proc. 33rd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1992, pp. 258-267.
6. M. DUBINER AND U. ZWICK, Contact networks, amplification and percolation, in preparation.
7. M. DUBINER AND U. ZWICK, How do read-once formulae shrink?, Combin. Probab. Comput., 3 (1994), pp. 455-469.
8. Q. GU AND A. MARUOKA, Amplification of bounded depth monotone read-once Boolean formulas. SIAM J. Comput., 20 (1991), pp. 41-55.
9. A. GUPTA AND S. MAHAJAN, Using amplification to compute majority with majority, manuscript, 1992.
10. J. HȦSTAD, A. RAZBOROV, AND A. YAO, On the shrinkage exponent for read-once formulae, Theoret. Comput. Sci., 141 (1995), pp. 260-282.
11. V. M. KHRAPCHENKO, Complexity of the realization of linear function in the class of π-circuits, Math. Notes Acad. Sci. USSR, 9 (1071), pp. 21-23.
12. V. M. KHRAPCHENKO, A method of determining lower bounds for the complexity of π-schemes, Math. Notes Acad. Sci. USSR, 10 (1071), pp. 474-479.
13. O. LUPANOV, On computing symmetric functions of the propositional calculus by switching networks, Problemy Kibernet., 15 (1965), pp. 85-100 (to Russian).
14. E. MOORE AND C. SHANNON, Reliable circuits using less reliable relays, J. Franklin Inst., 262 (1956), pp. 101-208 and 281-207.
15. M. PATERSON, N. PIPPENGER, AND U. ZWICK, Faster circuits and shorter formulae for multiple addition, multiplication and symmetric Boolean Functions, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 642-650.
16. M. PATERSON, N. PIPPENGER, AND U. ZWICK, Optimal carry save networks, in Boolean Function Complexity, M. Paterson,ed., London Mathematical Society Lecture Note Series, Vol. 169, Cambridge University Press, Cambridge, UK, 1992, pp. 174-201.
17. M. PATERSON AND U. ZWICK, Shrinkage of de Morgan formulae under restriction, Random Structures Algorithm, 4 (1993), pp. 135-150.
18. J. RADHAKRISHNAN AND K. SUBRAHMANYAM, Directed monotone contact networks for threshold functionts, Inform. Process. Lett., 50 (1994), pp. 100-203.
19. L. VALIANT, Short monotone formulae for the majority function, J. Algorithm, 5 (1984), pp. 363-388.