On the equivalence and containment problems for context-free languages
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LetG andG0 be context-free grammars. Necessary and sufficient conditions onG0 are obtained for the decidability ofL(G0)\( \subseteq \)L((G) It is also shown that it is undecidable for whichG0,L(G)\( \subseteq \) is decidable. Furthermore, given thatL(G)\( \subseteq \) is decidable for a fixedG0, there is no effective procedure to determine the algorithm which decidesL(G)\( \subseteq \) IfL(G0) is a regular set,L(G) = L(G0) is decidable if and only ifL(G0) is bounded. However, there exist non-regular, unboundedL(G0) for whichL(G) = L(G0) is decidable.
KeywordsComputational Mathematic Effective Procedure Containment Problem
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