On commutative context-free languages. (English) Zbl 0627.68063

Let \(\Sigma =\{a_ 1,a_ 2,...,a_ n\}\) be an alphabet and let \(L\subset \Sigma^*\) be the commutative image of \(FP^*\) where F and P are finite subsets of \(\Sigma^*\). If, for any permutation \(\sigma\) of \(\{\) 1,2,...,n\(\}\), \(L\cap a^*_{\sigma (1)}...a^*_{\sigma (n)}\) is context-free, then L is context-free. This theorem provides a solution to the Fliess conjecture in a restricted case. If the result could be extended to finite unions of the \(FP^*\) above, the Fliess conjecture could be solved.


68Q45 Formal languages and automata
Full Text: DOI


[1] {\scM. Fliess}, personal communication, 1970.
[2] Ginsburg, S., The mathematical theory of context-free languages, (1966), McGraw-Hill New York · Zbl 0184.28401
[3] Ginsburg, S., Algebraic and automata-theoretic properties of formal languages, (1975), North-Holland Amsterdam · Zbl 0325.68002
[4] Harrison, M.A., Introduction to formal language theory, (1978), Addison-Wesley Reading, MA · Zbl 0411.68058
[5] Maurer, H.A., The solution to a problem by Ginsburg, Inform. process. lett., 1, 7-10, (1971) · Zbl 0219.68036
[6] Oshiba, I., On permuting letters of words in context-free languages, Inform. and control, 20, 405-409, (1972) · Zbl 0247.68025
[7] Parikh, R.J., On context-free languages, J. assoc. comput. Mach., 13, 570-581, (1966) · Zbl 0154.25801
[8] Perrot, J.F., Sur la fermeture commutative des C-langages, (), 597-600 · Zbl 0168.25802
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.