Abstract
Classical algorithms convert arbitrary automata into regular expressions that have an exponential size in the size of the automaton. There exists a well-known family of automata, obtained by the Glushkov construction (of an automaton from an expression) and named Glushkov automata, for which the conversion is linear. Our aim is to extend the family of Glushkov automata. A first step for such an extension is to define a new family of regular operators and to check that the associated extended expressions have good properties: existence of normal forms, succinctness with respect to equivalent simple expressions, and compatibility with Glushkov functions. This paper addresses this first step and investigates the case of multi-tilde operators.
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References
McNaughton, R.F., Yamada, H.: Regular expressions and state graphs for automata. IEEE Transactions on Electronic Computers 9, 39–57 (1960)
Glushkov, V.M.: On a synthesis algorithm for abstract automata. Ukr. Matem. Zhurnal 12(2), 147–156 (1960) (in Russian)
Brzozowski, J.A., McCluskey, E.J.: Signal flow graph techniques for sequential circuit state diagrams. IEEE Trans. on Electronic Computers EC-12(2) (1963)
Hagenah, C., Muscholl, A.: Computing epsilon-free nfa from regular expressions in O(n log\(^{\mbox{2}}\)(n)) time. ITA 34(4), 257–278 (2000)
Hromkovic, J., Seibert, S., Wilke, T.: Translating regular expressions into small ε-free nondeterministic finite automata. J. Comput. Syst. Sci. 62(4), 565–588 (2001)
Brüggemann-Klein, A.: Regular expressions into finite automata. Theoret. Comput. Sci. 120(2), 197–213 (1993)
Champarnaud, J.M., Ziadi, D.: From c-continuations to new quadratic algorithms for automata synthesis. Internat. J. Algebra Comput. 11(6), 707–735 (2001)
Ilie, L., Yu, S.: Follow automata. Inf. Comput. 186(1), 140–162 (2003)
Delgado, M., Morais, J.: Approximation to the smallest regular expression for a given regular language. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 312–314. Springer, Heidelberg (2005)
Han, Y.S., Wood, D.: Obtaining shorter regular expressions from finite-state automata. Theor. Comput. Sci. 370(1-3), 110–120 (2007)
Ellul, K., Krawetz, B., Shallit, J., Wang, M.: Regular expressions: New results and open problems. Journal of Automata, Languages and Combinatorics 10(4), 407–437 (2005)
Ziadi, D.: Regular expression for a language without empty word. Theor. Comput. Sci. 163(1&2), 309–315 (1996)
Gelade, W., Neven, F.: Succinctness of the complement and intersection of regular expressions. In: Albers, S., Weil, P. (eds.) STACS. Dagstuhl Seminar Proceedings, vol. 08001, pp. 325–336 (2008)
Gruber, H., Holzer, M.: Finite automata, digraph connectivity, and regular expression size. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 39–50. Springer, Heidelberg (2008)
Gruber, H., Holzer, M.: Language operations with regular expressions of polynomial size. In: Câmpeanu, C. (ed.) 10th International Workshop on Descriptional Complexity of Formal Systems (DCFS 2008), Charlottetown, Canada, pp. 182–193 (2008)
Caron, P., Ziadi, D.: Characterization of Glushkov automata. Theoret. Comput. Sci. 233(1–2), 75–90 (2000)
Caron, P., Champarnaud, J.M., Mignot, L.: A new family of regular operators fitting with the position automaton computation. In: et al. (eds.) International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2009), S̋pindleruv Mýn, Czech Republic. LNCS (2009)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)
Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages. Word, Language, Grammar, vol. I, pp. 41–110. Springer, Berlin (1997)
Conway, J.H.: Regular algebra and finite machines. Chapman and Hall, Boca Raton (1971)
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Caron, P., Champarnaud, JM., Mignot, L. (2009). Multi-tilde Operators and Their Glushkov Automata. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2009. Lecture Notes in Computer Science, vol 5457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00982-2_25
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DOI: https://doi.org/10.1007/978-3-642-00982-2_25
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