Algorithms for Boolean function query properties

SIAM Journal on Computing

Volumn 32, Issue 5, 2003, Pages 1140-1157

  Aaronson, Scott ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Algorithm; Boolean function; Quantum computation; Query complexity; Truth table

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DIGITAL ARITHMETIC; TREES (MATHEMATICS);

QUANTUM COMPUTATION; QUERY COMPLEXITY; TRUTH TABLE;

BOOLEAN FUNCTIONS;

EID: 0345447069     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539700379644     Document Type: Article

References (24)

1. S. Aaronson, Quantum certificate complexity, in Proceedings of the 18th Annual IEEE Conference on Computational Complexity, Aarhus, Denmark, 2003, IEEE Press, Los Alamitos, CA, 2003, pp. 171-178.
2. S. Aaronson, Quantum lower bound for the collision problem, in Proceedings of the 34th ACM Symposium on Theory of Computing (STOC), Montreal, 2002, ACM, New York, 2002, pp. 635-642.
3. A. Ambainis, Quantum lower bounds by quantum arguments, J. Comput. System Sci., 64 (2002), pp. 750-767.
4. A. Ambainis and R. de Wolf, Average-case quantum query complexity, in Proceedings of the Symposium on Theoretical Aspects of Computing Science, 2000.
5. H. Barnum, M. Saks, and M. Szegedy, Quantum decision trees and semidefinite programming, in Proceedings of the 18th Annual IEEE Conference on Computational Complexity, Aarhus, Denmark, 2003, IEEE Press, Los Alamitos, CA, 2003, pp. 179-193.
6. Z. Bar-Yossef, R. Kumar, and D. Sivakumar, Sampling algorithms: Lower bounds and applications, in Proceedings of the 33rd ACM Symposium on Theory of Computing (STOC), Crete, 2001, ACM, New York, 2001, pp. 266-275.
7. R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf, Quantum lower bounds by polynomials, J. ACM, 48 (2001), pp. 778-797.
8. E. Bernstein and U. Vazirani, Quantum complexity theory, SIAM J. Comput., 26 (1997), pp. 1411-1473.
9. H. Buhrman and R. de Wolf, Complexity measures and decision tree complexity: A survey, Theoret. Comput. Sci., 288 (2002), pp. 21-43.
10. S. L. A. Czort, The Complexity of Minimizing Disjunctive Normal Form Formulas, Master's thesis, University of Aarhus, Aarhus, Denmark, 1999.
11. W. van Dam, Quantum oracle interrogation: Getting all the information for almost half the price, in Proceedings of the 39th IEEE Symposium on Foundations of Computer Science (FOCS), Palo Alto, CA, 1998, IEEE, Piscataway, NJ, 1998, pp. 362-367.
12. D. Guijarro, V. Lavín, and V. Raghavan, Exact learning when irrelevant variables abound, Inform. Process. Lett., 70 (1999), pp. 233-239.
13. L. K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the 28th ACM Symposium on Theory of Computing (STOC), Philadelphia, 1996, ACM, New York, 1996, pp. 212-219.
14. T. Hancock, T. Jiang, M. Li, and J. Tromp, Lower bounds on learning decision lists and trees, Inform. and Comput., 126 (1996), pp. 114-122.
15. K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall, Englewood Cliffs, NJ, 1971.
16. L. Hyafil and R. L. Rivest, Constructing optimal binary decision trees is NP-complete, Inform. Process. Lett., 5 (1976), pp. 15-17.
17. A. Yu. Kitaev, Quantum computations: Algorithms and error correction, Russian Math. Surveys, 52 (1997), pp. 1191-1249.
18. N. Nisan, Crew PRAMs and decision trees, SIAM J. Comput., 20 (1991), pp. 999-1007.
19. N. Nisan and M. Szegedy, On the degree of Boolean functions as real polynomials, Comput. Complexity, 4 (1994), pp. 301-313.
20. A. A. Razborov and S. Rudich, Natural proofs, J. Comput. System Sci., 55 (1997), pp. 24-35.
21. M. Saks and A. Wigderson, Probabilistic Boolean decision trees and the complexity of evaluating game trees, in Proceedings of the 27th IEEE Symposium on Foundations of Computer Science (FOCS), IEEE, Piscataway, NJ, 1986, pp. 29-38.
22. M. Santha, On the Monte Carlo decision tree complexity of read-once formulae, Random Structures Algorithms, 6 (1995), pp. 75-87.
23. D. Sieling, Minimization of decision trees is hard to approximate, in Proceedings of the 18th Annual IEEE Conference on Computational Complexity, Aarhus, Denmark, 2003, IEEE Press, Los Alamitos, CA, 2003, pp. 84-92.
24. R. Solovay, Lie groups and quantum circuits, talk presented at the Workshop on Mathematics of Quantum Computation, Mathematical Sciences Research Institute, Berkeley, CA, 2000.