Partial derivatives of regular expressions and finite automaton constructions

Theoretical Computer Science

Volumn 155, Issue 2, 1996, Pages 291-319

  Antimirov, Valentin ^a   Kucherov, G ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; COMPUTATIONAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

BRZOZOWSKI ALGORITHM; NON DETERMINISTIC FINITE AUTOMATA; PARTIAL DERIVATIVES; WORD DERIVATIVE;

FINITE AUTOMATA;

EID: 0030110111     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(95)00182-4     Document Type: Article

References (32)

1. V.M. Antimirov, Rewriting regular inequalities, December 1994, Proc. FCT'95, to be presented at the conf. Fundamentals of Computation Theory, August, 1995. in:
2. V.M. Antimirov, Partial derivatives of regular expressions and finite automata constructions, in: E.W. Mayr and C. Puech, eds., 12th Annual Symp. on Theoretical Aspects of Computer Science. Proceedings., Lecture Notes in Computer Science, Vol. 900 (Springer, Berlin, 1995) 455-466.
3. V.M. Antimirov and P.D. Mosses, Rewriting extended regular expressions, Theoret. Comput. Sci. 143 (1995) 51-72.
4. D. Benanav, D. Kapur and P. Narendran, Complexity of matching problems, J. Symbolic Comput. 3(1 & 2) (1987) 203-216.
5. G. Berry and R. Sethi, From regular expressions to deterministic automata, Theoretical Comput. Sci., 48:117-126, 1986.
6. J. Berstel, Finite automata and rational languages, an introduction, in: J. Pin, ed., Finite Automata and Applications, Lecture Notes in Computer Science, Vol. 386 (Springer, Berlin, 1987) 2-14.
7. A. Brüggemann-Klein, Regular expressions into finite automata, Theoret. Comput. Sci. 120 (1993) 197-213.
8. J.A. Brzozowski, Derivatives of regular expressions, J. ACM 11 (1964) 481-494.
9. J.A. Brzozowski and E.L. Leiss, On equations for regular languages, finite automata, and sequential networks, Theoret. Comput. Sci. 10 (1980) 19-35.
10. C.-H. Chang and R. Paige, From regular expressions to DFA's using compressed NFA's, in: A. Apostolico, M. Crochemore, Z. Galil and U. Manber, eds., Combinatorial Pattern Matching. Proceedings. Lecture Notes in Computer Science, Vol. 644 (Springer, Berlin, 1992) 88-108.
11. J.H. Conway, Regular Algebra and Finite Machines (Chapman and Hall, London, 1971).
12. N. Dershowitz and J.-P. Jouannaud, Rewrite systems, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol. B, Chap. 6. (Elsevier, Amsterdam; and MIT Press, Cambridge, MA, 1990).
13. A. Ginzburg, A procedure for checking equality of regular expressions, J. ACM 14(2) (1967) 355-362.
14. V.M. Glushkov, The abstract theory of automata, Russian Math. Surveys, 16 (1961) 1-53.
15. J.A. Goguen and J. Meseguer, Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations, Theoret. Comput. Sci. 105 (1992) 217-273.
16. J.A. Goguen and T. Winkler, Introducing OBJ3. Technical Report SRI-CSL-88-9, Computer Science Lab., SRI International, 1988.
17. R.M. Goldberg, Finite state automata from regular expression trees, Computer J. 36(7) (1993) 623-630.
18. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, Reading, MA, 1979).
19. D. Krob, Differentiation of K-rational expressions, Internat. J. Algebra Comput. 2(1) (1992) 57-87.
20. G. Kucherov and M. Rusinowitch, Complexity of testing ground reducibility for linear word rewriting systems with variables, in: Proc. 4th Internat. Workshop on Conditional and Typed Term Rewriting Systems, Jerusalem (Israel), July 1994. (To appear in the LNCS series).
21. G. Kucherov and M. Rusinowitch, On Ground-Reducibility Problem for word rewriting systems with variables, in: E. Deaton and R. Wilkerson, eds., Proc. 1994 ACMISIGAPP Symp. on Applied Computing, Phoenix (USA), 1994. (ACM-Press, New York, 1995).
22. R. McNaughton and H. Yamada, Regular expressions and state graphs for automata, IEEE Trans. on Electronic Computers, 9(1) (1960) 39-47.
23. Y. Mizoguchi, H. Ohtsuka and Y. Kawahara, A symbolic calculus of regular expressions, Bull. Inform. Cybernet. 22(3-4) (1987) 165-170.
24. J. Myhill, Finite automata and the representation of events, Technical Report WADD TR-57-624, Wright Patterson AFB, Ohio, 1957.
25. A. Nerode, Linear automaton transformations, in: Proc. AMS 9 (1958) 541-544.
26. D. Perrin, Finite automata, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol B, Chap. 1. (Elsevier, Amsterdam; and MIT Press, Cambridge, MA, 1990).
27. M.O. Rabin and D. Scott, Finite automata and their decision problems, IBM J. Res. Development 3(2) (1959) 114-125.
28. V.N. Redko, On defining relations for the algebra of regular events, Ukrain. Mat. Zh. 16 (1964) 120-126.
29. A. Salomaa, Theory of Automata (Pergamon, Oxford, 1969).
30. S. Sippu and E. Soisalon-Soininen, Parsing Theory. Vol. 1: Languages and Parsing, EATCS Monographs on Theoretical Computer Science (Springer, Berlin, 1988).
31. K. Thompson, Regular expression search algorithms, Comm. ACM 11(6) (1968) 419-422.
32. B.W. Watson, A taxonomy of finite automata construction algorithms, Computing Science Note 93/43, Eindhoven University of Technology, The Netherlands, 1993.