Abstract
It is known that Ogden lemma fails for the class of k-well-nested multiple context-free languages for \(k \ge 3\). In this article we prove a relaxed version of this lemma for linear well-nested MCFLs and show that its statement may be applied to generate counterexamples of linear well-nested MCFLs by the method already existing for the stronger variant.
The work was partly supported by the grant NSh-1423.2014.1 “Mathematical logic and algorithm theory.”
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Notes
- 1.
Following the Russian tradition, the author prefers the term “linear” to “non-branching”. However, he acknowledges the extreme ambiguity of this term. May be, some other term should be more proper.
- 2.
In [10] a more narrow definition of direct descendance was used. However, all the arguments of that paper are still valid for current definition.
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Sorokin, A. (2016). Ogden Property for Linear Displacement Context-Free Grammars. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2016. Lecture Notes in Computer Science(), vol 9537. Springer, Cham. https://doi.org/10.1007/978-3-319-27683-0_26
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