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Non-générateurs algébriques et substitution. (French) Zbl 0569.68060

We prove the following: given a rational cone \({\mathcal L}\) whose substitution closure is the largest sub-full AFL of the family of context-free languages, then \({\mathcal L}\) was already this subfamily.

MSC:

68Q45 Formal languages and automata
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References:

[1] 1. J.-M. AUTEBERT, J. BEAUQUIER, L. BOASSON, M. NIVAT, Quelques problèmes ouverts en théorie des langages algébriques, R.A.I.R.O. Informatique théorique, vol. 13, 1979, p. 363-379. Zbl0434.68056 MR556958 · Zbl 0434.68056
[2] 2. J. BERSTEL, Transductions and Context-Free Languages, Teubner Verlag, 1979. Zbl0424.68040 MR549481 · Zbl 0424.68040
[3] 3. L. BOASSON, The Inclusion of the Substitution Closure of Linear and One-Counter Languages in the Largest Sub-Full AFL of the Family of CFL’s is Proper, Information Proc. Letter, vol. 2, 1973, p. 135-140. Zbl0329.68067 MR345452 · Zbl 0329.68067
[4] 4. S. GREIBACH, Chains of Full AFL’S, Math. System Theory, vol. 4, 1970, p. 231-242. Zbl0203.30102 MR329324 · Zbl 0203.30102
[5] 5. M. LATTEUX, A propos du lemme de substitution, Theoretical Comp. Science, vol.14, 1981, p. 119-123. Zbl0454.68086 MR609517 · Zbl 0454.68086
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