Previous |  Up |  Next

Article

Title: The finite automata approaches in stringology (English)
Author: Holub, Jan
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 48
Issue: 3
Year: 2012
Pages: 386-401
Summary lang: English
.
Category: math
.
Summary: We present an overview of four approaches of the finite automata use in stringology: deterministic finite automaton, deterministic simulation of nondeterministic finite automaton, finite automaton as a model of computation, and compositions of finite automata solutions. We also show how the finite automata can process strings build over more complex alphabet than just single symbols (degenerate symbols, strings, variables). (English)
Keyword: exact pattern matching
Keyword: approximate pattern matching
Keyword: finite automata
Keyword: dynamic programming
Keyword: bitwise parallelism
Keyword: suffix automaton
Keyword: border array
Keyword: degenerate symbol
MSC: 62A10
MSC: 93E12
idMR: MR2975796
.
Date available: 2012-08-31T15:50:37Z
Last updated: 2013-09-24
Stable URL: http://hdl.handle.net/10338.dmlcz/142945
.
Reference: [1] Abrahamson, K.: Generalized string matching.SIAM J. Comput. 16 (1987), 6, 1039–1051. Zbl 0646.68079, MR 0917040, 10.1137/0216067
Reference: [2] Aho, A. V., Corasick, M. J.: Efficient string matching: an aid to bibliographic search.Commun. ACM 18 (1975), 6, 333–340. Zbl 0301.68048, MR 0371172, 10.1145/360825.360855
Reference: [3] Allauzen, C., Crochemore, M., Raffinot, M.: Factor oracle: A new structure for pattern matching.In: SOFSEM'99, Theory and Practice of Informatics (J. Pavelka, G. Tel, and M. Bartošek, eds.), Milovy 1999, Lect. Notes Comput. Sci. 1725 (1999), Springer-Verlag, Berlin, pp. 295–310. Zbl 0964.68078, MR 1784520
Reference: [4] Antoniou, P., Holub, J., Iliopoulos, C. S., Melichar, B., Peterlongo, P.: Finding common motifs with gaps using finite automata.In: Implementation and Application of Automata (O. H. Ibarra and H.-C. Yen, eds.), Lect. Notes Comput. Sci. 4094 (2006), Springer-Verlag, Heidelberg, pp. 69–77. Zbl 1160.68683, MR 2296448
Reference: [5] Baeza-Yates, R. A., Gonnet, G. H.: A new approach to text searching.Commun. ACM 35 (1992), 10, 74–82. 10.1145/135239.135243
Reference: [6] Baker, B. S.: Parameterized duplication in strings: algorithms and an application to software maintenance.SIAM J. Comput. 26 (1997), 5, 1343–1362. Zbl 0885.68085, MR 1471985, 10.1137/S0097539793246707
Reference: [7] Blumer, A., Blumer, J., Ehrenfeucht, A., Haussler, D., Chen, M. T., Seiferas, J.: The smallest automaton recognizing the subwords of a text.Theor. Comput. Sci. 40 (1985), 1, 31–44. Zbl 0574.68070, MR 0828515, 10.1016/0304-3975(85)90157-4
Reference: [8] Blumer, A., Blumer, J., Ehrenfeucht, A., Haussler, D., McConnel, R.: Complete inverted files for efficient text retrieval and analysis.J. Assoc. Comput. Mach. 34 (1987), 3, 578–595. MR 0904194, 10.1145/28869.28873
Reference: [9] Boyer, R. S., Moore, J. S.: A fast string searching algorithm.Commun. ACM 20 (1977), 10, 762–772. Zbl 1219.68165, 10.1145/359842.359859
Reference: [10] Cambouropoulos, E., Crochemore, M., Iliopoulos, C. S., Mouchard, L., Pinzon, Y. J.: Algorithms for computing approximate repetitions in musical sequences.In: Proc. Tenth Australian Workshop on Combinatorial Algorithms (R. Raman and J. Simpson, eds.), AWOCA'99, School of Computing, Curtin University of Technology, Perth 1999, pp. 129–144. Zbl 1008.68043
Reference: [11] Commentz-Walter, B.: A string matching algorithm fast on the average.In: Proc. 6th International Colloquium on Automata, Languages and Programming (H. A. Maurer, ed.), Graz 1979, Lect. Notes Comput. Sci. 71 (1979), Springer-Verlag, Berlin, pp. 118–132. Zbl 0407.68092
Reference: [12] Crochemore, M.: Transducers and repetitions.Theor. Comput. Sci. 45 (1986), 1, 63–86. Zbl 0615.68053, MR 0865967, 10.1016/0304-3975(86)90041-1
Reference: [13] Damerau, F.: A technique for computer detection and correction of spelling errors.Commun. ACM 7 (1964), 3, 171–176. 10.1145/363958.363994
Reference: [14] Dömölki, B.: An algorithm for syntactical analysis.Comput. Linguistics 3 (1964), 29–46, 1964.
Reference: [15] Fischer, M. J., Paterson, M.: String matching and other products.In: Proc. SIAM-AMS Complexity of Computation (R. M. Karp, ed.), Providence 1974, pp. 113–125. Zbl 0301.68027, MR 0400782
Reference: [16] Fredriksson, K., Mozgovoy, M.: Efficient parameterized string matching.Inf. Process. Lett. 100 (2006), 3, 91–96. Zbl 1185.68282, MR 2254198, 10.1016/j.ipl.2006.06.009
Reference: [17] Galil, Z.: Open problems in stringology.In: Combinatorial Algorithms on Words (A. Apostolico and Z. Galil, eds.), NATO ASI Series F 12 (1985), Springer-Verlag, Berlin, pp. 1–8. Zbl 0607.68054, MR 0815328
Reference: [18] Hamming, R. W.: Error detecting and error correcting codes.The Bell System Techn. J. 29 (1950), 2, 147–160. MR 0035935
Reference: [19] Holub, J.: Bit parallelism-NFA simulation.In: Implementation and Application of Automata (B. W. Watson and D. Wood, eds.), Lect. Notes in Comput. Sci. 2494 (2002), Springer-Verlag, Heidelberg, pp. 149–160. Zbl 1015.68524
Reference: [20] Holub, J.: Finite automata in pattern matching.In: Algorithms in Computational Molecular Biology: Techniques, Approaches and Applications (M. Elloumi and A. Y. Zomaya, eds.), John Wiley and Sons, 2011, pp. 51–71.
Reference: [21] Holub, J., Kadlec, T.: NFA simulation using deterministic state cache.In: London Algorithmics 2008: Theory and Practice (J. Chan, J. W. Daykin, and M. S. Rahman, eds.), College Publications 2009, pp. 152–166.
Reference: [22] Holub, J., Melichar, B.: Implementation of nondeterministic finite automata for approximate pattern matching.In: Proc. 3rd International Workshop on Implementing Automata, Rouen 1998, pp. 74–81.
Reference: [23] Holub, J., Melichar, B.: Approximate string matching using factor automata.Theor. Comput. Sci. 249 (2000), 2, 30–311. Zbl 0949.68088, MR 1798315, 10.1016/S0304-3975(00)00064-5
Reference: [24] Holub, J., Smyth, W. F.: Algorithms on indeterminate strings.In: Proc. 14th Australasian Workshop On Combinatorial Algorithms (M. Miller and K. Park, eds.), Seoul National University, Seoul 2003, pp. 36–45.
Reference: [25] Holub, J., Smyth, W. F., Wang, S.: Hybrid pattern-matching algorithms on indeterminate strings.In: London Stringology Day and London Algorithmic Workshop 2006 (J. Daykin, M. Mohamed, and K. Steinhoefel, eds.) King's College London Series Texts in Algorithmics 2007, pp. 115–133.
Reference: [26] Holub, J., Smyth, W. F., Wang, S.: Fast pattern-matching on indeterminate strings.J. Discret. Algorithms 6 (2008), 1, 37–50. Zbl 1162.68808, MR 2397082, 10.1016/j.jda.2006.10.003
Reference: [27] Holub, J., Špiller, P.: Practical experiments with NFA simulation.In: Proc. Eindhoven FASTAR Days 2004 (L. Cleophas and B. W. Watson, eds.), TU Eindhoven 2004, The Finite Automata Approaches in Stringology 15, pp. 73–95.
Reference: [28] Hopcroft, J. E., Ullman, J. D.: Introduction to automata, languages and computations.Addison-Wesley, Reading 1979. MR 0645539
Reference: [29] Huffman, D. A.: The synthesis of sequential switching circuits.J. Franklin Inst. 257 (1954), 161–190, 275–303. Zbl 0166.27201, MR 0062648, 10.1016/0016-0032(54)90574-8
Reference: [30] Huffman, D. A.: A method for the construction of minimum-redundancy codes.Proc. Inst. Radio Engrs 40 (1952), 9, 1098–1101. Zbl 0137.13605
Reference: [31] Iliopoulos, C. S., Jayasekera, I., Melichar, B., Šupol, J.: Weighted degenerated approximate pattern matching.In: Proc. 1st International Conference on Language and Automata Theory and Applications, Tarragona 2007.
Reference: [32] Kleene, S. C.: Representation of events in nerve nets and finite automata.Automata Studies (1956), 3–42. MR 0077478
Reference: [33] Knuth, D. E., Morris, J. H., Jr, Pratt, V. R.: Fast pattern matching in strings.SIAM J. Comput. 6 (1977), 2, 323–350. Zbl 0372.68005, MR 0451916, 10.1137/0206024
Reference: [34] Kurtz, S.: Reducing the space requirements of suffix trees.Softw. Pract. Exp. 29 (1999), 13, 1149–1171. 10.1002/(SICI)1097-024X(199911)29:13<1149::AID-SPE274>3.0.CO;2-O
Reference: [35] Lahoda, J., Melichar, B.: Pattern matching in text coded by finite translation automaton.In: Proc. 7th International Multiconference Information Society (M. Heričko et al., eds.), Institut Jožef Stefan, Ljubljana 2004, pp. 212–214.
Reference: [36] Lahoda, J., Melichar, B.: General pattern matching on regular collage system.In: Proc. Prague Stringology Conference'05 (J. Holub and M. Šimánek, eds.), Czech Technical University in Prague 2005, pp. 153–162.
Reference: [37] Levenshtein, V. I.: Binary codes capable of correcting deletions, insertions and reversals.Sov. Phys. Dokl. 6 (1966), 707–710. MR 0189928
Reference: [38] McCulloch, W. S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity.Bull. Math. Biophys. 5 (1943), 115–133. Zbl 0063.03860, MR 0010388, 10.1007/BF02478259
Reference: [39] Mealy, G. H.: A method for synthetizing sequential circuits.Bell System Techn. J. 34 (1955), 5, 1045–1079. MR 0073450, 10.1002/j.1538-7305.1955.tb03788.x
Reference: [40] Melichar, B.: Repetitions in text and finite automata.In: Proc. Eindhoven FASTAR Days 2004 (L. Cleophas and B. W. Watson, eds.), TU Eindhoven 2004, pp. 1–46.
Reference: [41] Melichar, B., Holub, J.: 6D classification of pattern matching problems.In: Proceedings of the Prague Stringology Club Workshop'97 (J. Holub, ed.), Czech Technical University in Prague, 1997, pp. 24–32. Collaborative Report DC-97-03.
Reference: [42] Melichar, B., Holub, J., Polcar, T.: Text searching algorithms. Vol. I: Forward string matching.Textbook for course Text Searching Algorithms, 2005.
Reference: [43] Moore, E. F.: Gedanken experiments on sequential machines.Automata Studies (1965), 129–153. MR 0078059
Reference: [44] Morris, J. H., Jr, Pratt, V. R.: A Linear Pattern-Matching Algorithm.Report 40, University of California, Berkeley 1970.
Reference: [45] Navarro, G., Raffinot, M.: A bit-parallel approach to suffix automata: Fast extended string matching.In: Proc. 9th Annual Symposium on Combinatorial Pattern Matching (M. Farach-Colton, ed.), Lect. Notes in Comput. Sci. 1448, Piscataway, NJ, 1998. Springer-Verlag, Berlin, pp. 14–33. MR 1672618
Reference: [46] Rabin, M. O., Scott, D.: Finite automata and their decision problems.IBM J. Res. Dev. 3 (1959) 114–125. Zbl 0158.25404, MR 0103795, 10.1147/rd.32.0114
Reference: [47] Sellers, P. H.: The theory and computation of evolutionary distances: Pattern recognition.J. Algorithms 1 (1980), 4, 359–373. Zbl 0454.68110, MR 0604870, 10.1016/0196-6774(80)90016-4
Reference: [48] Shyamasundar, R. K.: A Simple String Matching Algorithm.Technical Report, Tata Institute of Fundamental Research 1976.
Reference: [49] M. Šimůnek, Melichar, B.: Borders and finite automata.In: Implementation and Application of Automata (O. H. Ibarra and H.-C. Yen, eds.), Lecture Notes in Comput. Sci. 4094, Springer-Verlag, Heidelberg 2006, pp. 58–68. Zbl 1142.68416, MR 2296447
Reference: [50] Ukkonen, E.: Finding approximate patterns in strings.J. Algorithms 6 (1985), 1–3, 132–137. Zbl 0566.68072, MR 0780855, 10.1016/0196-6774(85)90023-9
Reference: [51] Voráček, M., Vagner, L., Rahman, S., Iliopoulos, C. S.: The constrained longest common subsequence problem for degenerate strings.In: Implementation and Application of Automata (J. Holub and J. Žďárek, eds.), Lecture Notes in Comput. Sci. 4783, Springer-Verlag, Heidelberg 2007, pp. 309–311. Zbl 1137.68621
Reference: [52] Wu, S., Manber, U.: Fast text searching allowing errors.Commun. ACM 35 (1992), 10, 83–91. 10.1145/135239.135244
Reference: [53] Ziv, J., Lempel, A.: Compression of individual sequences via variable length coding.IEEE Trans. Inf. Theory 24 (1978), 530–536. MR 0507465, 10.1109/TIT.1978.1055934
.

Files

Files Size Format View
Kybernetika_48-2012-3_4.pdf 444.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo