The Parikh functions of sparse context-free languages are quasi-polynomials

We prove that the Parikh map of a bounded context-free language is a box spline. Moreover we prove that in this case, such a function is rational.

[1]  Wolfgang Dahmen,et al.  The number of solutions to linear diophantine equations and multivariate splines , 1988 .

[2]  M. Schützenberger,et al.  Rational sets in commutative monoids , 1969 .

[3]  Benedetto Intrigila,et al.  On the structure of the counting function of sparse context-free languages , 2006, Theor. Comput. Sci..

[4]  C. Procesi,et al.  The algebra of the box-spline , 2006 .

[5]  Lucian Ilie,et al.  A characterization of poly-slender context-free languages , 2000, RAIRO Theor. Informatics Appl..

[6]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[7]  David Maier,et al.  Review of "Introduction to automata theory, languages and computation" by John E. Hopcroft and Jeffrey D. Ullman. Addison-Wesley 1979. , 1980, SIGA.

[8]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[9]  Juha Honkala,et al.  Decision problems concerning thinness and slenderness of formal languages , 1998, Acta Informatica.

[10]  Michel Latteux,et al.  On Bounded Context-free Languages , 1984, J. Inf. Process. Cybern..

[11]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

[12]  Danny Raz.  Length Considerations in Context-Free Languages , 1997, Theor. Comput. Sci..

[13]  Philippe Flajolet,et al.  Analytic Models and Ambiguity of Context-free Languages* , 2022 .

[14]  Michele Vergne,et al.  Residue formulae for vector partitions and Euler-MacLaurin sums , 2003, Adv. Appl. Math..

[16]  Oscar H. Ibarra,et al.  On Sparseness, Ambiguity and other Decision Problems for Acceptors and Transducers , 1986, STACS.

[17]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[18]  Roberto Incitti,et al.  The growth function of context-free languages , 2001, Theor. Comput. Sci..

[19]  Aldo de Luca,et al.  Finiteness and Regularity in Semigroups and Formal Languages , 1999, Monographs in Theoretical Computer Science An EATCS Series.

[20]  J. Sakarovitch.  Eléments de théorie des automates , 2003 .

[21]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[23]  Juha Honkala,et al.  A decision method for Parikh slenderness of context-free languages , 1996 .

[24]  Lucian Ilie.  On Generalized Slenderness of Context-Free Languages , 2001, Words, Semigroups, and Transductions.

[25]  Juha Honkala,et al.  On Parikh slender context-free languages , 2001, Theor. Comput. Sci..

[26]  Seymour Ginsburg,et al.  The mathematical theory of context free languages , 1966 .