Deterministic context-sensitive languages: Part I*

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A context-sensitive grammar G is said to be CS(k) iff a particular kind of table-driven parser, Tk(G), exists. Corresponding to each Tk(G), we define a class of parsers T¯k(G). Tk(G) is itself a T¯k(G). The main results are:

  • 1.

    Any processor T¯k(G) for a CS(k) grammar G accepts exactly the sentences of G.

  • 2.

    The set of languages generable by CS(k) grammars is exactly the set of languages accepted by deterministic linear-bounded automata (DLBA's).

  • 3.(a)

    It is undecidable whether there exists any k ⩾ 0 such that an arbitrary CSG is CS(k).

    • (b)

      For every fixed k ⩾ 0, there is no algorithm that will decide if G is CS(k) and also construct Tk(G) if it exists.

    • 4.

      For any DLBA M, algorithms are given to (i) construct a CS(k) grammar GM that generates the language accepted by M, and (ii) construct a processor T¯1(GM).

    • 5.

      CS(k) grammars are unambiguous.

    • 6.

      The sentences of a CS(k) grammar can be parsed in a time proportional to the length of their derivations.

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*

A preliminary version of this paper was presented at the Tenth Annual Symposium on Switching and Automata Theory, Waterloo, Ontario, October 15–17, 1969.