Abstract
In this paper, we start out by giving a characterization of the set R of the generating functions of a regular language. We then propose two algorithms able to determine if a rational function f(x) lies in R and which provide an unambiguous regular language for f(x). We discuss an open problem regarding languages having a rational generating function.
This work was partially supported by MURST project: Modelli di calcolo innovativi: metodi sintattici e combinatori.
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References
Banderier C., Bousquet-Mélou M., Denise A., Flajolet P., Gardy D., GouyouBeauchamps D.: On generating functions of generating trees. Proceedings of FPSAC99 11th Conference (1999) 40–52
Barcucci E., Del Lungo A., Pergola E., PinzaniR • ECO: a methodology for the Enumeration of Combinatorial Objects. Journal of Difference Equations and Applications 5 (1999) 435–490
Bassino F.: Star-height of an IN-rational series. STACS 96 LLNCS 1046 Springer (1996) 125–135
Berstel J., Perrin D.: Theory of codes. Academic Press (1985)
Berstel J., Reutenauer C.: Rational series and their languages. Springer-Verlag Berlin (1988)
Chomsky N., Schützenberger M.P.: The algebraic theory of context-free languages. Computer Programming and Formal Systems North-Holland Amsterdam (1963) 118–161
Cori R., Vauquelin B.: Planar maps are well labeled trees. Can. J. Math. 33 (1981) 1023–1042
Delest M., Viennot G.: Algebraic languages and polyominoes enumeration. Theoret. Comput. Sci. 34 (1984) 169–206
Eilenberg S.: Automa, Languages, and Machines. Academic Press A New York (1974)
Gourdon X., Salvy B.: Effective asymptotics of linear recurrences with rational coefficients. Discrete Mathematics 153 (1996) 145–163
Hoperoft J.E., Ullman J.D.: Introduction to automata theory, languages, and computation. Reading Massachussets (1979)
Krob D.: Eléments de. combinatoire. Magistère 1-ère année Ecole Normale Superieure (1995)
Pan V.: Algebraic complexity of computing polynomial zeroes. Comput. Math. Appl. (1987) 285–304
Perrin D.: On positive matrices. Theoret. Comput. Sci. 94 (1992) 357–366
Riordan J.: Combinatorial identities. John Wiley & Sons Inc. New York
Salomaa A., Soittola M.: Automata-theoretic aspects of formal power series. Springer-Verlag New York (1978)
Soittola M.: On DOL synthesis problem. Automata, languages, development. North Holland Amsterdam (1976) 313–321
Soittola M.: Positive rational sequences. Theoret. Comput. Sci. 2 (1976) 317–322
West J.: Generating trees and the Catalan and Schröeder numbers. Discrete Math. 146 (1995) 247–262
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Barcucci, E., Del Lungo, A., Frosini, A., Rinaldi, S. (2000). From Rational Functions to Regular Languages. In: Krob, D., Mikhalev, A.A., Mikhalev, A.V. (eds) Formal Power Series and Algebraic Combinatorics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04166-6_62
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DOI: https://doi.org/10.1007/978-3-662-04166-6_62
Publisher Name: Springer, Berlin, Heidelberg
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