Complexity and Probability of Some Boolean Formulas

Combinatorics Probability and Computing

Volumn 7, Issue 4, 1998, Pages 451-463

  Savický, Petr ^a  

^a INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032251279     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548398003630     Document Type: Article

References (12)

1. Buss, S. R. and Bonet, M. L. (1994) Size-depth tradeoffs for Boolean formulae. IPL 11 151-155.
2. Friedman, J. (1992) Probabilistic spaces of Boolean functions of a given complexity: generalities and random k-SAT coefficients. Research Report CS-TR-387-92, Princeton University.
3. Lefmann, H. and Savicky, P. (1997) Some typical properties of large AND/OR Boolean formulas. Random Struct. Alg. 10 337-351.
4. Razborov, A. A. (1988) Bounded-depth formulae over {∧, ⊕} and some combinatorial problems. In Complexity of Algorithms and Applied Mathematical Logic (in Russian), Ser. Voprosy Kibernetiky (Problems in Cybernetics), (S. I. Adian, ed.), Moscow, pp. 149-166.
5. Riordan J. and Shannon, C. E. (1942) The number of two terminal series-parallel networks. J. Math. Phys. 21 83-93.
6. Savický, P. (1990) Random Boolean formulas representing every Boolean function with asymptotically equal probability. Discrete Math. 83 95-103.
7. Savický, P. (1995) Bent functions and random Boolean formulas. Discrete Math. 147 211-234.
8. Savicky, P. (1995) Improved Boolean formulas for the Ramsey graphs. Random Struct. Alg. 6 407-415.
9. Savický, P. and Woods, A. R. The number of Boolean functions computed by formulas of a given size. To appear in Random Struct. Alg.
10. Valiant, L. G. (1984) Short monotone formulae for the majority function. J. Algorithms 5 363-366.
11. Wegener, I. (1987) The Complexity of Boolean Functions, Wiley-Teubner Series in Computer Science.
12. Woods, A. R. (1997) Coloring rules for finite trees, and probabilities of monadic second order sentences. Random Struct. Alg. 10 453-485.