Bounded depth arithmetic circuits: Counting and closure

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

Volumn 1644 LNCS, Issue , 1999, Pages 149-158

  Allender, Eric ^a   Ambainis, Andris ^b   Barrington, David A Mix ^c   Datta, Samir ^a   Lêthanh, Huong ^d  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Biologically Inspired Neural and Dynamical Systems Laboratory   (United States)

^d UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; TIMING CIRCUITS;

ARITHMETIC CIRCUIT; CLOSURE PROPERTY; COMPUTATIONAL POWER; FUNCTION CLASS; LOWER BOUNDS; THRESHOLD CIRCUITS;

LOGIC CIRCUITS;

EID: 84887465752     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48523-6_12     Document Type: Conference Paper

References (24)

1. [Al97] E. Allender, Making computation count: Arithmetic circuits in the nineties. In the Complexity Theory Column, edited by Lane Hemaspaandra, SIGACT NEWS 28, 4:2-15, December 1997.
2. [AAD97] M. Agrawal, E. Allender, S. Datta, On TC0; AC0 and arithmetic circuits. In Proceedings of the 12th Annual IEEE Conference on Computational Complexity, pp:134-148, 1997.
3. [ABL98] A. Ambainis, D. M. Barrington, H. LeThanh, On counting AC0 circuits with negative constants. In Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS), 1998.
4. [ABFR91] J. Aspnes, R. Beigel, M. Furst, S. Rudich, The expressive power of voting polynomials. In Proceedings of the 23th ACM Symposium on Theory of Computing (STOC), pp:402-409, 1991.
5. [AJ93] C. Alvarez, B. Jenner, A very hard logspace counting class. Theoretical Com- puter Science, 107:3-30, 1993.
6. [AJMV98] E. Allender, J. Jiao, M. Mahajan, and V. Vinay, Non-commutative arithme- Tic circuits: depth reduction and size lower bounds, Theoretical Computer Science, 209:47-86, 1998.
7. [Ba89] D. A. Barrington, Bounded-Width Polynomial-Size Branching Programs Re- cognize Exactly Those Languages in NC1. Journal of Computer and System Sciences 38(1):150-164, 1989.
8. [BLMS98] D. M. Barrington, Ch-J Lu, P. B. Miltersen, S. Skyum, Searching constant width mazes captures the AC0 Hierarchy. In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, 1998.
9. [BRS91] R. Beigel, N. Reingold, D. Spielman, The perceptron strikes back. In Proceedings of the 6th Annual IEEE Structure in Complexity Theory Conference, 1991.
10. [CMTV96] H. Caussinus, P. McKenzie, D. Thfierien, H. Vollmer, Nondeterministic NC1Computation. In Proceedings of the 11th Annual IEEE Conference on Computational Complexity, pp:12-21, 1996.
11. [Gu90] Y. Gurevich. Matrix decomposition Problem is complete for the average case. In Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp:802-811, 1990.
12. [Ha86] J. Hastad, Almost optimal lower bounds for small depth circuits. In Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing, pp:6-20, 1986.
13. [FKPS85] R. Fagin, M. Klawe, N. Pippenger, and L. Stockmeyer. Bounded-depth, polynomial-size circuits for symmetric functions. Theoretical Computer Science, 36:239-250, 1985.
14. [LeT98] H. LeThanh, Circuits Arithmfietiques de Profondeur Constante, Thesis, Uni- versitffe Paris Sud, 1998.
15. [Lu98] C. J. Lu, An exact characterization of symmetric functions in qAC02. In Proceedings of the 4th Annual International Computing and Combinatorics Conference (COCOON), 1998.
16. [MV97] M. Mahajan, V.Vinay, A combinatorial algorithm for the determinant. Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp:730-738, 1997.
17. [NS98] F. Noilhan and M. Santha, Semantical Counting Circuits, submitted, 1998.
18. [OH93] M. Ogiwara, L. Hemachandra, A complexity theory for feasible closure properties. Journal of Computer and System Sciences, 46(3):295-325, June 1993.
19. [Ra87] A. A. Razborov, Lower bound on size of bounded depth networks over a complete basis with logical addition. Mathematicheskie Zametki, 41:598-607, 1987. English translation in Mathematical Notes of the Academy of Sciences of the USSR, 41:333-338, 1987.
20. [Tod92a] S. Toda, Counting problems computationally equivalent to the determinant. Manuscript.
21. [Tod92b] S. Toda, Classes of arithmetic circuits capturing the complexity of compu- Ting the determinant. IEICE Transactions, Informations and Systems, E75:116-124, 1992.
22. [Val79] L. Valiant, The complexity of computing the permanent. Theoretical Computer Science, 8:189-201, 1979.
23. [Ven92] H. Venkateswaran, Circuit definitions of non-deterministic complexity classes. SIAM Journal on Computing, 21:655-670, 1992.
24. [Vin91] V. Vinay, Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In Proceedings of the 6th Annual IEEE Structure in Complexity Theory Conference, pp:270-284, 1991.