Abstract
Antimirov and Mosses proposed a rewrite system for deciding the equivalence of two (extended) regular expressions. In this paper we present a functional approach to that method, prove its correctness, and give some experimental comparative results. Besides an improved version of Antimirov and Mosses’s algorithm, we present a version using partial derivatives. Our preliminary results lead to the conclusion that, indeed, these methods are feasible and, generally, faster than the classical methods.
This work was partially funded by Fundação para a Ciência e Tecnologia (FCT) and Program POSI, and by project ASA (PTDC/MAT/65481/2006).
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References
Antimirov, V.M., Mosses, P.D.: Rewriting extended regular expressions. In: Rozenberg, G., Salomaa, A. (eds.) Developments in Language Theory, pp. 195–209. World Scientific, Singapore (1994)
Almeida, M., Moreira, N., Reis, R.: On the performance of automata minimization algorithms. Technical Report DCC-2007-03, DCC - FC & LIACC, Universidade do Porto (June 2007)
Antimirov, V.M.: Partial derivatives of regular expressions and finite automation constructions. Theor. Comput. Sci. 155(2), 291–319 (1996)
Brzozowski, J.A.: Derivatives of regular expressions. Journal of the Association for Computing Machinery 11(4), 481–494 (1964)
Ellul, K., Shallit, J., Wang, M.: Regular expressions: New results and open problems. In: The DCFS 2002 conference, London, Ontario (2002)
Hopcroft, J., Karp, R.M.: A linear algorithm for testing equivalence of finite automata. Technical Report TR 71 -114, University of California, Berkeley, California (1971)
Hopcroft, J., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (2000)
Ilie, L., Yu, S.: Follow automata. Inf. Comput. 186(1), 140–162 (2003)
Kozen, D.C.: A completeness theorem for Kleene algebras and the algebra of regular events. Infor. and Comput. 110(2), 366–390 (1994)
Kozen, D.C.: Automata and Computability. Undergrad. Texts in Computer Science. Springer, Heidelberg (1997)
Kuich, W., Salomaa, A.: Semirings, Automata, Languages, vol. 5. Springer, Heidelberg (1986)
Mairson, H.G.: Generating words in a context-free language uniformly at random. Information Processing Letters 49, 95–99 (1994)
Reis, R., Moreira, N., Almeida, M.: On the representation of finite automata. In: Mereghetti, C., Palano, B., Pighizzini, G., Wotschke, D. (eds.) Proc. of DCFS 2005, Como, Italy, pp. 269–276 (2005)
Salomaa, A.: Two complete axiom systems for the algebra of regular events. Journal of the Association for Computing Machinery 13(1), 158–169 (1966)
Shallit, J.: Regular expressions, enumeration and state complexity. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317. Springer, Heidelberg (2005)
Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time: Preliminary report. In: Conf. Record of 5th Annual ACM Symposium on Theory of Computing, Austin, Texas, USA, pp. 1–9. ACM, New York (1973)
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Almeida, M., Moreira, N., Reis, R. (2008). Antimirov and Mosses’s Rewrite System Revisited. In: Ibarra, O.H., Ravikumar, B. (eds) Implementation and Applications of Automata. CIAA 2008. Lecture Notes in Computer Science, vol 5148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70844-5_6
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DOI: https://doi.org/10.1007/978-3-540-70844-5_6
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