Nondeterministic finite automata recent results on the descriptional and computational complexity

International Journal of Foundations of Computer Science

Volumn 20, Issue 4, 2009, Pages 563-580

  Holzer, Markus ^a,b   Kutrib, Martin ^a  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Computational complexity; Descriptional complexity; Nondeterministic finite automata

Indexed keywords

EID: 68649099218     PISSN: 01290541     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129054109006747     Document Type: Conference Paper

References (80)

1. Adorna, H.N.: 3-party message complexity is better than 2-party ones for proving lower bounds on the size of minimal nondeterministic finite automata. J. Autom., Lang. Comb. 7 (2002) 419-432
2. Adorna, H.N.: Some descriptional complexity problems in finite automata theory. In: Philippine Computing Science Congress. Computing Society of the Philippines (2005) 27-32
3. Amilhastre, J., Janssen, P., Vilarem, M.C.: FA minimisation heuristics for a class of finite languages. In: Workshop on Implementing Automata (WIA 1999). Number 2214 in LNCS, Springer (2001) 1-12
4. Berman, P., Lingas, A.: On the complexity of regular languages in terms of finite automata. Technical Report 304, Polish Academy of Sciences (1977)
5. Birget, J.C.: Intersection and union of regular languages and state complexity. Inform. Process. Lett. 43 (1992) 185-190
6. Birget, J.C.: Partial orders on words, minimal elements of regular languages and state complexity. Theoret. Comput. Sci. 119 (1993) 267-291
7. Birget, J.C.: Erratum: Partial orders on words, minimal elements of regular languages and state complexity. Available at: http://clam.rutgers.edu/ ∼birget/papers.html (2002)
8. Birget, J.C.: State-complexity of finite-state devices, state compressibility and incom-pressibility. Math. Systems Theory 26 (1993) 237-269
9. Björklund, H., Martens, W.: The tractability frontier for NFA minimization. In: International Colloqium on Automata, Languages and Propgramming (ICALP 2008). Number 5126 in LNCS, Springer (2008) 27-38
10. Bordihn, H., Holzer, M., Kutrib, M.: State complexity of NFA to DFA conversion for subregular language families. In: Descriptional Complexity of Formal Systems (DCFS 02008). University of Prince Edward Island, Canada (2008) 85-96
11. Bordihn, H., Holzer, M., Kutrib, M.: Determinization of Nondeterministic Finite Automata Subclasses. Submitted for publication (2008)
12. Câmpeanu, C., Ĉulik, K., Salomaa, K., Yu, S.: State complexity of basic operations on finite languages. In: Workshop on Implementing Automata (WIA 1999). Number 2214 in LNCS, Springer (2001) 60-70
13. Chrobak, M.: Finite automata and unary languages. Theoret. Comput. Sci. 47 (1986) 149-158
14. Chrobak, M.: Errata to "finite automata and unary languages". Theoret. Comput. Sci. 302 (2003) 497-498
15. Domaratzki, M., Salomaa, K.: Lower bounds for the transition complexity of NFAs. In: Mathematical Foundations of Computer Science (MFCS 2006). Number 4162 in LNCS, Springer (2006) 315-325
16. Domaratzki, M., Salomaa, K.: Transition complexity of language operations. Theoret. Comput. Sci. 387 (2007) 147-154
17. Domaratzki, M., Okhotin, A.: State complexity of power. TUCS Technical Report 845, Turku Centre for Computer Science (2008)
18. Ellul, K.: Descriptional complexity measures of regular languages. Master's thesis, University of Waterloo (2002)
19. Geffert, V.: (Non)determinism and the size of one-way finite automata. In: Descrip-tional Complexity of Formal Systems (DCFS 2005). Rapporto Tecnico 06-05, Univer-sità degli Studi di Milano (2005) 23-37
20. Geffert, V.: Magic numbers in the state hierarchy of finite automata. Inform. Comput. 205 (2007) 1652-1670
21. Glaister, I., Shallit, J.: A lower bound technique for the size of nondeterministic finite automata. Inform. Process. Lett. 59 (1996) 75-77
22. Goldstine, J., Kappes, M., Kintala, C.M.R., Leung, H., Malcher, A., Wotschke, D.: Descriptional complexity of machines with limited resources. J. UCS 8 (2002) 193-234
23. Gramlich, G.: Probabilistic and nondeterministic unary automata. In: Mathematical Foundations of Computer Science (MFCS 2003). Number 2747 in LNCS, Springer (2003) 460-469
24. Gramlich, G.: Über die algorithmische Komplexität regulärer Sprachen. Doctoral Dissertation, Johann Wolfgang-Goethe- Univeristät, Frankfurt am Main (2007)
25. Gramlich, G., Schnitger, G.: Minimizing NFA's and regular expressions. In: Symposium on Theoretical Aspects of Computer Science (STACS 2005). Number 3404 in LNCS, Springer (2005) 399-411
26. Gruber, H., Holzer, M.: A note on the number of transitions of nondeterministic finite automata. In: Theorietag "Automaten und Formale Sprachen." Universität Tübingen (2005) 24-25
27. Gruber, H., Holzer, M.: Finding lower bounds for nondeterministic state complexity is hard. In: Developments in Language Theory (DLT 2006). Number 4036 in LNCS, Springer (2006) 363-374
28. Gruber, H., Holzer, M.: Computational complexity of NFA minimization for finite and unary languages. In: Language and Automata Theory and Applications (LATA). Technical Report 35/07, Universitat Rovira i Virgili, Tarragona (2007) 261-272
29. Gruber, H., Holzer, M.: Inapproximability of nondeterministic state and transition complexity assuming P ≠ NP. In: Developments in Language Theory (DLT 2007). Number 4588 in LNCS, Springer (2007) 205-216
30. Gruber, H., Holzer, M.: Results on the average state and transition complexity of finite automata accepting finite languages. Theoret. Comput. Sci. 387 (2007) 155- 166
31. 2 n) time. RAIRO Inform. Théor. 34 (2000) 257-277
32. Han, Y.S., Salomaa, K.: State complexity of union and intersection of finite languages. In: Developments in Language Theory (DLT 2007). Number 4588 in LNCS, Springer (2007) 217-228
33. Havel, I.M.: The theory of regular events II. Kybernetica 6 (1969) 520-544
34. Holzer, M., Salomaa, K., Yu, S.: On the state complexity of k-entry deterministic finite automata. J. Autom., Lang. Comb. 6 (2001) 453-466
35. Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Int. J. Found. Comput. Sci. 14 (2003) 1087-1102
36. Hopcroft, J.E.: An n log n algorithm for minimizing the state in a finite automaton. In: The Theory of Machines and Computations. Academic Press (1971) 189-196
37. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley (1979)
38. Hromkoviĉ, J.: Communication Complexity and Parallel Computing. Springer (1997)
39. Hromkoviĉ, J.: Descriptional complexity of finite automata: Concepts and open problems. J. Autom., Lang. Comb. 7 (2002) 519-531
40. Hromkoviĉ, J., Seibert, S., Karhumäki, J., Klauck, H., Schnitger, G.: Communication Complexity Method for Measuring Nondeterminism in Finite Automata. Inform. Comput. 172 (2002) 201-217
41. Hromkoviĉ, J., Schnitger, G.: Comparing the size of NFAs with and without ε-transitions. Theoret. Comput. Sci. 380 (2007) 100-114
42. Hromkoviĉ, J., Seibert, S., Wilke, T.: Translating regular expressions in small ε-free nondeterministic finite automata. J. Comput. System Sci. 62 (2001) 565-588
43. Iwama, K., Kambayashi, Y., Takaki, K.: Tight bounds on the number of states of DFAs that are equivalent to n-state NFAs. Theoret. Comput. Sci. 237 (2000) 485-494
44. n - α deterministic states. Theoret. Comput. Sci. 301 (2003) 451-462
45. Jiang, T., McDowell, E., Ravikumar, B.: The structure and complexity of minimal NFAs over a unary alphabet. Int. J. Found. Comput. Sci. 2 (1991) 163-182
46. Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22 (1993) 1117-1141
47. Jirásek, J., Jirásková, G., Szabari, A.: State Complexity of Concatenation and Complementation. Int. J. Found. Comput. Sci. 16 (2005) 511-529
48. Jirasek, J., Jiraskova, G., Szabari, A.: Deterministic blow-ups of minimial nondeterministic finite automata over a fixed alphabet. In: Developments in Language Theory (DLT 2007). Number 4588 in LNCS, Springer (2007) 254-265
49. Jirásková, G.: Note on minimal finite automata. In: Mathematical Foundations of Computer Science (MFCS 2001). Number 2136 in LNCS, Springer (2001) 421-431
50. Jirásková, G.: Note on minimal automata and uniform communication protocols. In: Grammars and Automata for String Processing. Taylor and Francis (2003) 163-170
51. Jirásková, G.: State complexity of some operations on binary regular languages. Theoret. Comput. Sci. 330 (2005) 287-298
52. Jirásková, G., Okhotin, A.: State complexity of cyclic shift. RAIRO Inform. Théor. 42 (2008) 335-360
53. Kameda, T., Weiner, P.: On the state minimization of nondeterministic finite automata. IEEE Trans. Comput. C-19 (1970) 617-627
54. Kapoutsis, C.A.: Removing bidirectionality from nondeterministic finite automata. In: Mathematical Foundations of Computer Science (MFCS 2005). Number 3618 in LNCS, Springer (2005) 544-555
55. Kari, J.: Personal communication (2006)
56. Landau, E.: Über die Maximalordnung der Permutationen gegebenen Grades. Archiv der Math. und Phys. 3 (1903) 92-103
57. Landau, E.: Handbuch der Lehre von der Verteilung der Primzahlen. Teubner (1909)
58. Leiss, E.: Succinct representation of regular languages by Boolean automata. Theoret. Comput. Sci. 13 (1981) 323-330
59. Lifshits, Y.: A lower bound on the size of ε-free NFA corresponding to a regular expression. Inform. Process. Lett. 85 (2003) 293-299
60. Malcher, A.: Minimizing finite automata is computationally hard. Theoret. Comput. Sci. 327 (2004) 375-390
61. Mandl, R.: Precise bounds associated with the subset construction on various classes of nondeterministic finite automata. In: Princeton Conference on Information and System Sciences. (1973) 263-267
62. Mera, F., Pighizzini, G.: Complementing unary nondeterministic automata. Theoret. Comput. Sci. 330 (2005) 349-360
63. Mereghetti, C., Pighizzini, G.: Optimal simulations between unary automata. SIAM J. Comput. 30 (2001) 1976-1992
64. Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: IEEE Symposium on Switching and Automata Theory (SWAT 1971). IEEE Press (1971) 188-191
65. Moore, F.R.: On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata. IEEE Trans. Comput. 20 (1971) 1211-1214
66. Nicaud, C.: Average state complexity of operations on unary automata. In: Mathematical Foundations of Computer Science (MFCS 1999). Number 1672 in LNCS, Springer (1999) 231-240
67. Pighizzini, G., Shallit, J.: Unary language operations, state complexity and Jacob-sthal's function. Int. J. Found. Comput. Sci. 13 (2002) 145-159
68. Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3 (1959) 114-125
69. Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two way finite automata. In: Symposium on Theory of Computing (STOC 1978). ACM Press (1978) 275-286
70. Salomaa, A., Wood, D., Yu, S.: On the state complexity of reversals of regular languages. Theoret. Comput. Sci. 320 (2004) 315-329
71. Salomaa, K., Yu, S.: NFA to DFA transformation for finite languages over arbitrary alphabets. J. Autom., Lang. Comb. 2 (1997) 177-186
72. Schnitger, G.: Regular expressions and NFAs without ε-transitions. In: Symposium on Theoretical Aspects of Computer Science (STACS 2006). Number 3884 in LNCS, Springer (2006) 432-443
73. Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM J. Res. Dev. 3 (1959) 198-200
74. Sipser, M.: Lower bounds on the size of sweeping automata. J. Comput. System Sci. 21 (1980) 195-202
75. Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Symposium on Theory of Computing (STOC 1973). ACM Press (1973) 1-9
76. Tamm, H.: On transition minimality of bideterministic automata. In: Developments in Language Theory (DLT 2007). Number 4588 in LNCS, Springer (2007) 411-421
77. Yu, S.: Regular languages. In: Handbook of Formal Languages. Volume 1. Springer (1997) 41-110
78. Yu, S.: State complexity of regular languages. J. Autom., Lang. Comb. 6 (2001) 221-234
79. Yu, S.: State complexity of finite and infinite regular languages. Bull. EATCS 76 (2002) 142-152
80. Yu, S., Zhuang, Q., Salomaa, K.: The state complexities of some basic operations on regular languages. Theoret. Comput. Sci. 125 (1994) 315-328