On the Complexities of Linear LL(1) and LR(1) Grammars

  title={On the Complexities of Linear LL(1) and LR(1) Grammars},
  author={Markus Holzer and Klaus-J{\"o}rn Lange},
Several notions of deterministic linear languages are considered and compared with respect to their complexities and to the families of formal languages they generate. We exhibit close relationships between simple linear languages and the deterministic linear languages both according to Nasu and Honda and to Ibarra, Jiang, and Ravikumar. Deterministic linear languages turn out to be special cases of languages generated by linear grammars restricted to LL(1) conditions, which have a membership… 
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A close lower bound is established: for certain LL(k)-linear grammars with n nonterminal symbols, every equivalent LL(1)-linear grammar must have at least \(n \cdot (m-1)^{2k-O(\log k)}\) nonTerminal symbols.
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A tape hardest deterministic context-free language is described and the best upper bound known on the tape complexity of (deterministic) context- free languages is (log(n) 2).
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The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory.
Some Subclasses of Context-Free Languages In NC1
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A study of these finite-turn pda and the context free languages they recognize and their characterized both in terms of grammars and generation from finite sets by three operations.
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On Uniformity within NC¹