Hidden word statistics

Journal of the ACM

Volumn 53, Issue 1, 2006, Pages 147-183

  Flajolet, Philippe ^a   Szpankowski, Wojciech ^b,d   Vallée, Brigitte ^a,c  

^a INRIA ROCQUENCOURT   (France)

^b PURDUE UNIVERSITY   (United States)

^c UNIVERSITÉ DE CAEN   (France)

^d Purdue University   (United States)

Author keywords

Combinatorial calculus; Complex asymptotics; De Bruijn graph; Discrete probability; Distributional analysis; Generating functions; Languages; Pattern matching; Subsequences; Words

Indexed keywords

COMBINATORIAL MATHEMATICS; DATA PROCESSING; FORMAL LANGUAGES; PATTERN MATCHING; TEXT PROCESSING;

COMPLEX ASYMPTOTICS; DE BRUIJN GRAPH; DISCRETE PROBABILITY; DISTRIBUTIONAL ANALYSIS; GENERATING FUNCTIONS; LANGUAGES; SUBSEQUENCES; WORDS;

PROBLEM SOLVING;

EID: 33745224501     PISSN: 00045411     EISSN: 00045411     Source Type: Journal    
DOI: 10.1145/1120582.1120586     Document Type: Article

References (49)

1. ABHYANKAR, S.-S. 1990. Algebraic Geometry for Scientists and Engineers. American Mathematical Society Providence, R.I.
2. ACZEL, A. 2000. The Mystery of the Aleph. Mathematics, the Kabbalah, and the Search for Infinity, Four Walls Eight Windows, New York.
3. APOSTOLICO, A., AND ATALLAH, M. 2002. Compact recognizers of episode sequences. Inf. Comput. 174, 2(May), 180-192.
4. ATALLAH, M., GWADERA, R., AND SZPANKOWSKI, W. 2003. Reliable detection of episodes in event sequences. In Proceedings of the 3rd IEEE International Conference on Data Mining (ICDM-03) (Melbourne, FL), Nov. IEEE Computer Science Press, Los Alamitos, CA, 67-74.
5. BENDER, E. A. 1973. Central and local limit theorems applied to asymptotic enumeration. J. Combinat. Theory 15, 91-111.
6. BENDER, E. A., AND KOCHMAN, F. 1993. The distribution of subword counts is usually normal. Europ. J. Combinat. 14, 265-275.
7. BENDER, E. A., RICHMOND, L. B., AND WILLIAMSON, S. G. 1983. Central and local limit theorems applied to asymptotic enumeration. III. Matrix recursions. J. Combinat. Theory, Ser. A 35, 3, 264-278.
8. BILLINGSLEY, P. 1986. Probability and Measure, 2nd Ed., John Wiley, New York.
9. BOASSON, L., CEGIELSKI, P., GUESSARIAN, I., AND MATIYASEVICH, Y. 1999. Window-accumulated subsequence matching problem is linear. In Proceedings of the 18th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems PODS, ACM, New York, 327-336.
10. BOURDON, J., AND VALLÉE, B. 2002. Generalized pattern matching statistics. In Proceedings of the Colloquium on Mathematics and Computer Science (Versailles, France). B. Chauvin et al. Eds. Birkhäuser Verlag, pp. 229-245.
11. CLÉMENT, J., FLAJOLET, P., AND VALLÉE, B. 2001. Dynamical sources in information theory: A general analysis of trie structures. Algorithmica, 29, 307-369.
12. CROCHEMORE, M., AND RYTTER, W. 1994. Text Algorithms, Oxford University Press, New York.
13. DAS, G., FLEISCHER, R., GASIENIEC, L., GUNOPULOS, D., AND KÄRKKÄINEN, J. 1997. Episode matching, In Combinatorial Pattern Matching, 8th Annual Symposium, Lecture Notes in Computer Science. 12-27.
14. DEN HOLLANDER, F. 2000. Large Deviations. American Mathematical Society, Providence, RI.
15. FLAJOLET, P., KIRSCHENHOFER, P., AND TICHY, R. 1988. Deviations from uniformity in random strings. Prob. Theory Rel. Fields 80, 139-150.
16. FLAJOLET, P., AND SEDGEWICK, R. 2005. Analytic Combinatorics, In prep., (Available electronically at http: algo.inria.fr/flajolet/Publications.)
17. FLAJOLET, P., AND SORIA, M. 1993. General combinatorial schemas: Gaussian limit distributions and exponential tails. Discr. Math. 114, 159-180.
18. GANTMACHER, F. R. 1986. Matrizentheorie. Deutscher Verlag der Wissenschaften, Berlin, Germany. (A translation of the Russian original Teoria Matriz, Nauka Moscow, Russia, 1966.)
19. GNEDENKO, B. V., AND KOLMOGOROV, A. N. 1968. Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Reading, MA.
20. GUIBAS, L., AND ODLYZKO, A. M. 1981a. Periods in strings. J. Combinat. Theory Ser. A, 30, 19-43.
21. GUIBAS, L., AND ODLYZKO, A. M. 1981b. String overlaps, pattern matching, and nontransitive games. J. Combinat. Theory Ser. A, 30, 183-208.
22. GUIVARC'H, Y. 2000. Marches aléatoires sur les groupes. Fascicule de probabilités. Publ. Inst. Rech. Math. Rennes.
23. GWADERA, R., ATALLAH, M., AND SZPANKOWSKI, W. 2004. Detection of significant sets of episodes in event sequences. In Proceedings of the 4th IEEE International Conference on Data Mining (ICDM-04) (Brighton, UK, Nov.) IEEE Computer Science Press, Los Alamitos, CA, 3-10.
24. GWADERA, R., ATALLAH, M., AND SZPANKOWSKI, W. 2005. Markov models for identification of significant episodes. In Proceedings of the 2005 SIAM International Conference on Data Mining (SDM-05) (Newport Beach, Cal. Apr.). SIAM, Philadelphia, PA.
25. HWANG, H.-K. 1996. Large deviations for combinatorial distributions: I. Central limit theorems, Ann. Appl. Prob. 6, 297-319.
26. HWANG, H.-K. 1998. On convergence rates in the central limit theorems for combinatorial structures, Europ. J. Combinat. 19, 329-343.
27. JANSON, S. 1997. Gaussian Hilbert spaces, Cambridge University Press, Cambridge, MA.
28. JANSON, S. 2004. Large deviations for sums of partially dependent random variables. Rand. Struct. Algorithms 24, 234-248.
29. KATO, T. 1980. Perturbation theory for Linear Operators. Springer-Verlag, New York.
30. KNUTH, D. E. 1997. The Art of Computer Programming, Fundamental Algorithms, Vol. 1, 3rd Ed., Addison-Wesley, Reading, MA.
31. KNUTH, D.E. 1998. The Art of Computer Programming. Sorting and Searching, Vol. 3, 2nd Ed., Addison-Wesley, Reading, MA.
32. KUCHEROV, G., AND RUSINOWITCH, M. 1997. Matching a set of strings with variable length don't cares. Theoret. Comput. Sci. 178, 129-154.
33. KUMAR, S., AND SPAFFORD, E. H. 1994. A pattern-matching model for intrusion detection. In Proceedings of the National Computer Security Conference. 11-21.
34. LOTHAIRE, M. 2005. Applied Combinatorics on Words. In Encyclopedia of Mathematics and Its Applications, vol. 90. Cambridge University Press, Cambridge, MA.
35. MCKAY, B. D., BAR-NATAN, D., BAR-HILLEL, M., AND KALAI, G. 1999. Solving the Bible code puzzle, Statistical Science, 14, 150-173.
36. NICODÈME, P., SALVY, B., AND FLAJOLET, P. 1999. Motif statistics. In Proceedings of the European Symposium on Algorithms. IEEE Computer Society Press, Los Alamitos, CA, No. 1643. 194-211.
37. PEVZNER, P. 2000. Computational Molecular Biology: An Algorithmic Approach, MIT Press, Cambridge, MA.
38. RÉGNIER, M., AND SZPANKOWSKI, W. 1997. On the approximate pattern occurrences in a text. In Proceedings of the Compression and Complexity of Sequences, IEEE Computer Society Press, Los Alamitos, CA, 253-264.
39. RÉGNIER, M., AND SZPANKOWSKI, W. 1998. On pattern frequency occurrences in a Markovian sequence. Algorithmica 22, 631-649.
40. RIGOUTSOS, I., FLORATOS, A., PARIDA, L., GAO, Y., AND PLATT, D. 2000. The emergence of pattern discovery techniques in computational biology. Metab. Eng. 2, 159-177.
41. SEDGEWICK, R., AND FLAJOLET, P. 1995. An Introduction to the Analysis of Algorithms, Addison-Wesley, Reading, MA.
42. STEELE, J. M. 1997. Probability Theory and Combinatorial Optimization. SIAM, Philadelphia, PA.
43. SZPANKOWSKI, W. 2001. Average Case Analysis of Algorithms on Sequences. Wiley, New York.
44. VALLÉE, B. 2001. Dynamical sources in information theory: Fundamental intervals and word prefixes. Algorithmica 29, 262-306.
45. VANET, A., MARSAN, L., AND SAGOT, M.-F. 1999. Promoter sequences and algorithmical methods for identifying them. Res. Microbiol. 150, 779-799.
46. WATERMAN, M. 1995. Introduction to Computational Biology. Chapman and Hall, London, England.
47. WESPI, A., DEBAR, H., DACIER, M., AND NASSEHI, M. 2000. Fixed vs. variable-length patterns for detecting suspicious process behavior. J. Comput. Secur. 8, 159-181.
48. WITZTUM, D., RIPS, E., AND ROSENBERG, Y. 1994. Equidistant letter sequences in the book of genesis. Stat. Sci. 9, 429-438.
49. WU, S., AND MANBER, U. 1995. Fast text searching allowing errors. Commun. ACM 35, 10 (Oct.), 83-91.