Abstract
Prefix-free words of a given language L can be obtained within the frame of the classical problem of random words. If

is the number of prefix-free words of length n of L, we find here the functional equation verified by the generating function

of the

’s, and solve this problem with exact and asymptotic formulas, for two kinds of languages : the two-sided well-balanced parentheses over the alphabet A={a1, ... am, ā1, ām}, and the palindroms over A={a1, ... am}.
Keywords
- Classical Problem
- Formal Language Theory
- Left Factor
- Random Word
- Minimum Modulus
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
J. BEAUQUIER-"Prefix and perfect languages"-Proceedings of the 8th C.A.A.P. (Italy 1983)-Lecture Notes in Computer Science 159, pp 129–140.
E.A. BENDER "-Asymptotic methods in enumeration"-SIAM Review Vol 16, no4 October 1974
J. BERSTEL-"Transductions and context-free languages"-Teubner Verlag (1979)
J. BEAUQUIER, L. THIMONIER-" Formal languages and Bernoulli processes"-To appear in "Algebra, Combinatorics and Logic in Computer science"-Colloquia Mathematica Soc.J. Bolyai (Hungary 1983) vol 42, North Holland.
J. BEAUQUIER, L. THIMONIER-" Computability of probabilistic parameters for some classes of formal languages"-Proceedings of the 11th Symposium Mathematical Foundations of Computer Science (Czechoslovakia 1984) Lecture Notes in Computer Science 176, pp. 194–204
J. BEAUQUIER, L. THIMONIER-"On formal languages, probabilities, paging and decoding algorithms"-Proceedings of the 5th Conference Fundamentals of Computing Theory (German Democratic Republic 1985)-Lecture Notes in Computer Science 199, pp 44–52
N. CHOMSKY, M.P. SCHUTZENBERGER-"The algebraic theory of context-free languages"-Computer programming and formal systems pp. 118–161 North Holland (1963)
L. COMTET-"Analyse Combinatoire"-PUF Paris (1970)
P. ERDOS, A. RENYI-"On a classical problem of probability theory"-Publ. M.I. Hung. Acad. Sci., 6(1961), 215–20
W. FELLER-"An introduction to probability theory and its applications"-J. Wiley (1968)
P. FLAJOLET-"Ambiguity and transcendence"-Proceedings of the 12th I.C.A.L.P. (Greece 1985) To appear in Lecture Notes in Computer Science.
P. FLAJOLET, M. REGNIER, D.SOTTEAU-" Algebraic methods for trie statistics"-To appear in Annuals of Discrete Math. (1984)
P. FLAJOLET, N.SAHEB-" The complexity of generating an exponentially distributed variable"-To appear in Journal of Algorithms (1985)
I.P.GOULDEN, D.M. JACKSON-"Combinatorial Enumeration"-J. Wiley (1983)
J. GOLDSTINE-"Substitution and bounded languages"-Journ of Comp. and Syst. Sciences 6 (1972) pp. 9–29
M.A. HARRISON-"Introduction to formal languages theory"-Add. Wesley (1978)
P.ENRICI-"Applied Computational and Complex analytis"-J.Wiley (vol 1: 1974; vol 2: 1977)
W. KUICH-"On the entropy of context-free languages"-Information and control 16, pp 173–200 (1970)
R. SEDGEWICK-" Mathematical Analysis of Combinatorial Algorithms"-In G. Louchard, G. Latouche ed., Probability theory and Computer Science, Acad. Press (1983)
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© 1986 Springer-Verlag
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Beauquier, J., Thimonier, L. (1986). Prefix-free words of length N over M letters : two-sided well-balanced parentheses and palindroms. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072506
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DOI: https://doi.org/10.1007/BFb0072506
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