Algebraic property testing: The role of invariance

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2008, Pages 403-412

  Kaufman, Tali ^a   Sudan, Madhu ^b  

^a IAS   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Error correcting codes; Locally testable codes; Sublinear time algorithms

Indexed keywords

AFFINE TRANSFORMATIONS; ALGEBRAIC FUNCTIONS; ALGEBRAIC PROPERTIES; DEGREE LINEAR; DO-MAINS; FUNCTIONS MAPPINGS; INVARIANT PROPERTIES; LINEAR PROPERTIES; LINEAR TRANSFORMATIONS; LOCAL CONSTRAINTS; LOCALLY TESTABLE CODES; LOWER BOUNDS; NECESSARY AND SUFFICIENT CONDITIONS; STRUCTURAL PARAMETERS; SUBLINEAR TIME ALGORITHMS; SYSTEMATIC STUDIES; TESTING RESULTS; UPPER AND LOWER BOUNDS; UPPER BOUNDS; VECTOR SPACES;

ARTIFICIAL INTELLIGENCE; CHARACTERIZATION; CODES (SYMBOLS); CONTROL THEORY; INFORMATION THEORY; PROBABILITY DENSITY FUNCTION;

FUNCTIONS;

EID: 57049100995     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. N. Alon, E. Fischer, I. Newman, and A. Shapira. A combinatorial characterization of the testable graph properties: It's all about regularity. STOC 2006, pages 251-260.
2. N. Alon, T. Kaufman, M. Krivelevich, S. Litsyn, and D. Ron. Testing low-degree polynomials over GF(2). RANDOM 2003, pages 188-199.
3. E. Ben-Sasson, P. Harsha, and S. Raskhodnikova. Some 3CNF properties are hard to test. STOC 2003 pages 345-354.
4. M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. JCSS, 47(3):549-595, 1993.
5. A. Bogdanov, K. Obata, and L. Trevisan. A lower bound for testing 3-colorability in bounded-degree graphs. FOCS 2002, pages 93-102.
6. C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós, B. Szegedy, and K. Vesztergombi. Graph limits and parameter testing. STOC 2006, pages 261-270.
7. S. D. Cohen. Functions and polynomials in vector spaces. Archiv der Mathematik, 48(5):409-419, May 1987.
8. R Delsarte, J.M. Goethals, and F.J. Mac Williams. On generalized Reed-Muller codes and their relatives. Information and Control, 16(5):403-442, 1970.
9. A. M. Frieze and R. Kannan. Quick approximation to matrices and applications. Combinatorica, 19(2): 175-220, 1999.
10. O. Goldreich, S. Goldwasser, and D. Ron. Property testing and its connection to learning and approximation. JACM, 45(4):653-750, 1998.
11. O. Goldreich and O. Sheffet. On the randomness complexity of property testing. RANDOM 2007, pages 509-524.
12. E. Grigorescu, T. Kaufman, and M. Sudan. 2-transitivity is insufficient for local testability. CCC 2008 page (to appear).
13. C. S. Jutla, A. C. Patthak, A. Rudra, and D. Zuckerman. Testing low-degree polynomials over prime fields. FOCS 2004, pages 423-432.
14. T. Kasami, S. Lin, and W. W. Peterson. New generalization of the Reed-Muller codes - Part I: Primitive codes. IEEE Trans. Inf. Th, 14:189-199, 1968.
15. T. Kaufman and S. Litsyn. Almost orthogonal linear codes are locally testable. FOCS 2005, pages 317-326.
16. T. Kaufman and D. Ron. Testing polynomials over general fields. FOCS 2004, pages 413-422.
17. T. Kaufman and M. Sudan. Algebraic property testing: the role of invariance. ECCC Technical Report, TR07-111, 2007.
18. R. Rubinfeld. Robust functional equations and their applications to program testing. SICOMP, 28(6): 1972-1997, 1999.
19. R. Rubinfeld and M. Sudan. Robust characterizations of polynomials with applications to program testing. SICOMP, 25(2):252-271, April 1996.