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nLab > Latest Changes: context-sensitive grammar

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    • CommentRowNumber1.
    • CommentAuthoralexis.toumi
    • CommentTimeNov 24th 2020

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorThomas Holder
    • CommentTimeNov 24th 2020
    • (edited Nov 24th 2020)

    I added an example of a context-sensitive language.

    By the way, this seems to be the definition of a grammar that is context-sensitive with erasing which are actually of type 0. A context-sensitive grammar has β∈(V+X) +\beta\in (V+X)^+ and (possibly) a controlled epsilon introduction rule s→εs\to\epsilon. I also suspect that V∩X=∅V\cap X=\emptyset is required here.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthoralexis.toumi
    • CommentTimeNov 24th 2020
    You're right, I forgot about the empty right-hand sides and about generating the empty string.
    For the requirement that $V \cap X = \emptyset$, I was implicitly assuming that the union $V + X$ is disjoint, so even if they had symbols in common these would be distinguished. Better make that explicit.

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