A limit law for outputs in random recursive circuits

Algorithmica (New York)

Volumn 31, Issue 3, 2001, Pages 403-412

  Tsukiji, T ^a   Mahmoud, H ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

Central limit theorem; Random structure

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; PROBABILITY; RANDOM PROCESSES;

RANDOM RECURSIVE CIRCUITS;

LOGIC CIRCUITS;

EID: 0242333232     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-001-0044-4     Document Type: Article

References (18)

1. Arya, S., Golin, M., and Mehlhorn, K. (2000). On the expected depth of random circuits. Combinatorics, Probability and Computing, 8, 209-228.
2. Athreya, K., and Karlin, S. (1968). Embedding of urn schemes into a continuous time Markov branching process and related limit theorems. Annals of Mathematical Statistics, 39, 1801-1817.
3. Athreya, K., and Key, P. (1972). Branching Processes. Springer-Verlag, New York.
4. Balcázar, J., Díaz, J., and Gabarró, J. (1995). Structural Complexity I. Springer-Verlag, Berlin.
5. Balińska, K., Quintas, L., and Szymański, J. (1994). Random recursive forests. Random Structures and Algorithms, 5, 3-12.
6. Díaz, J., Serna, M., Spirakis, P., and Torán, J. (1994). On the expected depth of boolean circuits. Technical Report LSI-94-7-R, Universitat Politècnica de Catalunya, Barcelona.
7. Eggenberger, F., and Pólya, G. (1923). Über die statistik verketetter vorgäge. Zeitschrift für Angewandte Mathematik und Mechanik, 1, 279-289.
8. Hall, P., and Heyde, C. (1980). Martingale Limit Theory and Its Applications. Academic Press, New York.
9. Johnson, N., and Kotz, S. (1977). Urn Models and Their Applications. Wiley, New York.
10. Kotz, S., Mahmoud, H., and Robert, P. (2000). On generalized Pólya urn models. Statistics and Probability Letters, 49, 163-173.
11. Mahmoud, H., and Smythe, R. (1992). Asymptotic joint normality of out-degrees of nodes in random recursive trees. Random Structures and Algorithms, 3, 255-266.
12. Mahmoud, H., and Smythe, R. (1995). Probabilistic analysis of bucket recursive trees. Theoretical Computer Science, 144, 221-249.
13. Mahmoud, H., Smythe, R., and Szymański, J. (1993). On the structure of plane-oriented recursive trees and their branches. Random Structures and Algorithms, 4, 151-176.
14. Pemantle, R. (1990). Nonconvergence to unstable points in urn models and stochastic approximations. Annals of Probability, 18, 698-712.
15. Smythe, R. (1996). Central limit theorems for urn models. Stochastic Processes and Their Applications, 65, 115-137.
16. Smythe, R., and Mahmoud, H. (1996). A survey of recursive trees. Theory of Probability ant Mathematical Statistics, 51, 1-29.
17. Tsukiji, T., and Xhafa, F. (1996). On the depth of randomly generated circuits, in Lecture Notes in Computer Science, Algorithms - ESA '96, Fourth Annual European Symposium, Vol. 1136, pp. 208-220. Díaz, J., and Serna, M., Eds. Springer-Verlag, Berlin.
18. Valiant, L. (1994). Circuits of the Mind. Oxford University Press, Oxford.