Complexity and limiting ratio of boolean functions over implication

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5162 LNCS, Issue , 2008, Pages 347-362

  Fournier, Hervé ^a   Gardy, Danièle ^a   Genitrini, Antoine ^a   Gittenberger, Bernhard ^b  

^a UNIVERSITY OF VERSAILLES   (France)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Analytic combinatorics; Boolean functions; Complexity; Implicational formulas; Limiting ratio; Probability distribution

Indexed keywords

BOOLEAN FUNCTIONS;

ANALYTIC COMBINATORICS; ASYMPTOTIC PROBABILITIES; BOOLEAN EXPRESSIONS; COMPLEXITY; IMPLICATIONAL FORMULAS; LIMITING RATIO; LOGICAL SYSTEM; SIMPLE EXPRESSION;

PROBABILITY DISTRIBUTIONS;

EID: 54249160967     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-85238-4_28     Document Type: Conference Paper

References (26)

1. Zaionc, M.: Statistics of implicational logic. Electronic Notes in Theoretical Computer Science 84 (2003)
2. Kostrzycka, Z., Zaionc, M.: Statistics of intuitionnistic versus classical logic. Studia Logica 76(3), 307-328 (2004)
3. Gardy, D.: Random boolean expressions. In: Colloquium on Computational Logic and Applications (2006)
4. Fournier, H., Gardy, D., Genitrini, A., Zaionc, M.: Classical and intuitionistic logic are asymptotically identical. In: CSL, pp. 177-193 (2007)
5. Paris, J.B., Vencovská, A., Wilmers, G.M.: A natural prior probability distribution derived from the propositional calculus. Annals of Pure and Applied Logic 70, 243-285 (1994)
6. Lefmann, H., Savický, P.: Some typical properties of large And/Or Boolean formulas. Random Structures and Algorithms 10, 337-351 (1997)
7. Woods, A.R.: Coloring rules for finite trees, and probabilities of monadic second order sentences. Random Struct. Algorithms 10(4), 453-485 (1997)
8. Chauvin, B., Flajolet, P., Gardy, D., Gittenberger, B.: And/Or trees revisited. Combinatorics, Probability and Computing 13(4-5), 475-497 (2004)
9. Moczurad, M., Tyszkiewicz, J., Zaionc, M.: Statistical properties of simple types. Mathematical Structures in Computer Science 10(5), 575-594 (2000)
10. Kostrzycka, Z.: On the density of truth of implicational parts of intuitionistic and classical logics. J. of Applied Non-Classical Logics 13(2) (2003)
11. Zaionc, M.: On the asymptotic density of tautologies in logic of implication and negation. Reports on Mathematical Logic 39, 67-87 (2005)
12. Kostrzycka, Z.: On the density of truth in modal logics. In: Mathematics and Computer Science, Nancy (France); Proceedings in DMTCS (September 2006) (to appear)
13. Matecki, G.: Asymptotic density for equivalence. Electronic Notes in Theoretical Computer Science 140, 81-91 (2005)
14. Kostrzycka, Z.: On asymptotic divergency in equivalential logics. Mathematical Structures in Computer Science 18, 311-324 (2008)
15. Woods, A.: On the probability of absolute truth for and/or formulas. Bulletin of Symbolic Logic 12(3) (2005)
16. Kozi C., J.: Subcritical pattern languages for and/or trees. Technical report (2008)
17. Valiant, L.: Short monotone formulae for the majority function. Journal of Algorithms 5, 363-366 (1984)
18. Boppana, R.B.: Amplification of probabilistic boolean formulas. In: Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, pp. 20-29 (1985)
19. Gupta, A., Mahajan, S.: Using amplification to compute majority with small majority gates. Comput. Complex. 6(1), 46-63 (1997)
20. Savicky, P.: Random Boolean formulas representing any Boolean function with asymptotically equal probability. Discrete Mathematics 83, 95-103 (1990)
21. Brodsky, A., Pippenger, N.: The boolean functions computed by random boolean formulas or how to grow the right function. Random Structures and Algorithms 27, 490-519 (2005)
22. Drmota, M.: Systems of functional equations. Random Structures and Algorithms 10(1-2), 103-124 (1997)
23. Lalley, S.P.: Finite range random walk on free groups and homogeneous trees. The Annals of Probability 21 (1993)
24. Flajolet, P., Sedgewick, R.: Analytic combinatorics: Functional equations, rational and algebraic functions. Technical Report 4103, INR. IA (January 2001)
25. Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (to appear, 2008) Available from the authors' web page
26. Pivoteau, C., Salvy, B., Soria, M.: Combinatorial Newton iteration to compute Boltzmann oracle. Technical report, Journées ALÉA (March 2008), http: //www-calf or. Iip6. f r/pivoteau