Abstract
This survey paper reviews the means that allow to go from one representation of the languages to the other and how, and to what extend, one can keep them small. Some emphasis is put on the comparison between the expressions that can be computed from a given automaton and on the construction of the derived term automaton of an expression.
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References
Eilenberg, S.: Automata, Languages, and Machines, vol. A. Academic Press, London (1974)
Berstel, J.: Transductions and Context-free Languages. B. G. Teubner (1979)
McNaughton, R., Yamada, H.: Regular expressions and state graphs for automata. IRE Trans. Electronic Computers 9, 39–47 (1960)
Wood, D.: Theory of Computation. John Wiley, Chichester (1987)
Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–111. Elsevier, Amsterdam (1997)
Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall, Boca Raton (1971)
Krob, D.: Complete systems of B-rational identities. Theoret. Computer Sci. 89, 207–343 (1991)
Sakarovitch, J.: Eléments de théorie des automates. Vuibert, English translation: Elements of Automata Theory, Cambridge University Press, Cambridge (to appear, 2003)
Brzozowski, J.A., McCluskey, E.J.: Signal flow graph techniques for sequential circuit state diagrams. IEEE Trans. Electronic Computers 12, 67–76 (1963)
Lombardy, S., Régis-Gianas, Y., Sakarovitch, J.: Introducing Vaucanson. CIAA 2003 328, 67–76 (2004); Journal version of Proc. of CIAA 2003, Lect. Notes in Comp. Sc. 2759, pp. 96–107 (2003) (with R. Poss)
Delgado, M.: 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)
Claveirole, T., Lombardy, S., O’Connor, S., Pouchet, L.-N., Sakarovitch, J.: Inside vaucanson. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 116–128. Springer, Heidelberg (2006)
Glushkov, V.M.: The abstract theory of automata. Russian Math. Surveys 16, 1–53 (1961)
Caron, P., Flouret, M.: Glushkov construction for multiplicities. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 52–61. Springer, Heidelberg (2001)
Lombardy, S., Sakarovitch, J.: Derivatives of rational expressions with multiplicity. Theor. Comput. Sci. 332, 141–177 (2005)
Thompson, K.: Regular expression search algorithm. Comm. Assoc. Comput. Mach. 11, 419–422 (1968)
Brzozowski, J.A.: Derivatives of regular expressions. J. Assoc. Comput. Mach. 11, 481–494 (1964)
Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theor. Comput. Sci. 155, 291–319 (1996)
Berry, G., Sethi, R.: From regular expressions to deterministic automata. Theor. Comput. Sci. 48, 117–126 (1986)
Berstel, J., Pin, J.E.: Local languages and the Berry-Sethi algorithm. Theor. Comput. Sci. 155, 439–446 (1996)
Champarnaud, J.M., Ziadi, D.: Canonical derivatives, partial derivatives and finite automaton constructions. Theor. Comput. Sci. 289, 137–163 (2002)
Brügemann-Klein, A.: Regular expressions into finite automata. Theor. Comput. Sci. 120, 197–213 (1993)
Hagenah, C., Musholl, A.: Computing ε-free NFAs from regular expressions in O(nlog2(n)) time. Theoret. Inform. Appl. 34, 257–277 (2000)
Hromkovic, J., Seibert, S., Wilke, T.: Translating regular expressions into small ε-free nondeterministic finite automata. J. Comput. System Sci. 62, 565–588 (2001)
Ilie, L., Yu, S.: Constructing NFAs by optimal use of positions in regular expressions. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 279–288. Springer, Heidelberg (2002)
Champarnaud, J.M., Nicart, F., Ziadi, D.: Computing the follow automaton of an expression. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 90–101. Springer, Heidelberg (2005)
Caron, P., Ziadi, D.: Characterization of Glushkov automata. Theor. Comput. Sci. 233, 75–90 (2000)
Lombardy, S., Sakarovitch, J.: How expressions can code for automata. Theoret. Inform. App. 39, 217–237 (2005)
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Sakarovitch, J. (2006). The Language, the Expression, and the (Small) Automaton. In: Farré, J., Litovsky, I., Schmitz, S. (eds) Implementation and Application of Automata. CIAA 2005. Lecture Notes in Computer Science, vol 3845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11605157_2
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DOI: https://doi.org/10.1007/11605157_2
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