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On the equivalence and containment problems for context-free languages

Abstract

LetG andG 0 be context-free grammars. Necessary and sufficient conditions onG 0 are obtained for the decidability ofL(G 0)\( \subseteq \) L((G) It is also shown that it is undecidable for whichG 0,L(G) \( \subseteq \) is decidable. Furthermore, given thatL(G) \( \subseteq \) is decidable for a fixedG 0, there is no effective procedure to determine the algorithm which decidesL(G) \( \subseteq \) IfL(G 0) is a regular set,L(G) = L(G 0) is decidable if and only ifL(G 0) is bounded. However, there exist non-regular, unboundedL(G 0) for whichL(G) = L(G 0) is decidable.

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References

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    S. Greibach, A note on undecidable properties of formal languages. SDC Document TM-738/038/00, August 1967.

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    S. Ginsburg andE. H. Spanier, BoundedAlgol-like languages,Trans. Amer. Math. Soc. 113 (1964), 333–368.

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Hopcroft, J.E. On the equivalence and containment problems for context-free languages. Math. Systems Theory 3, 119–124 (1969). https://doi.org/10.1007/BF01746517

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Keywords

  • Computational Mathematic
  • Effective Procedure
  • Containment Problem