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

@inproceedings{Holzer1993OnTC,
  title={On the Complexities of Linear LL(1) and LR(1) Grammars},
  author={Markus Holzer and Klaus-J{\"o}rn Lange},
  booktitle={FCT},
  year={1993}
}
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… 
On LL(k) linear conjunctive grammars
TLDR
This paper investigates the LL(k) subclass of linear conjunctive grammars, defined by analogy with the classical LL( k) Grammars: these are grammar that admit top-down linear-time parsing with k-symbol lookahead, and a parser for these grammARS that works in linear time and uses logarithmic space is constructed.
On the Transformation of LL(k)-linear Grammars to LL(1)-linear
TLDR
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.
Underlying Principles and Recurring Ideas of Formal Grammars
TLDR
The paper investigates some of the fundamental ideas of the context-free grammar theory, as they are applied to several extensions and subclasses of context- Free Grammar, including multi-component grammars, tree-adjoining grammARS, conjunctivegrammars and Boolean Grammars.
Inferring Deterministic Linear Languages
TLDR
This work compares several definitions of deterministic linear grammars, and for a reasonable definition prove the existence of a canonical normal form, and obtains positive learning results in case of polynomial learning from a given set of both positive and negative examples.
On the Complexity of Membership and Counting in Height-Deterministic Pushdown Automata
TLDR
This work investigates the membership and counting problems for generalizations of visibly pushdown automata, defined using the notion of height-determinism and shows that, when the stack-height of a given push down automaton can be computed using a finite transducer, both problems have the same complexity as for visibly push down languages.
Word Problems and Membership Problems on Compressed Words
TLDR
A fixed deterministic context-free language with a PSPACE-complete compressed membership problem for finitely presented monoids and completeness results for complexity classes in the range from P to EXPSPACE are obtained.
Deterministic Biautomata and Subclasses of Deterministic Linear Languages
TLDR
This work proposes the notion of a deterministic biautomaton, a machine reading an input word from both ends of deterministic linear languages, and uses its characterizations to establish closure properties of the studied subclasses of languages.
...
...

References

SHOWING 1-10 OF 21 REFERENCES
Simple Deterministic Languages
TLDR
The s-languages are those languages recognized by a particular restricted form of deterministic pushdown automaton, called an s-machine, and it is shown that they have the prefix property, and that they include the regular sets with end-markers.
On the Translation of Languages from Left to Right
  • D. Knuth
  • Computer Science, Linguistics
    Inf. Control.
  • 1965
A Note on Tape-Bounded Complexity Classes and Linear Context-Free languages
TLDR
The equivalence of the following statements, for 0 g ~ < 1, m shown by describing a log(n)-complete hnear language, is shown.
On the Tape Complexity of Deterministic Context-Free Languages
TLDR
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).
Formal languages and their relation to automata
  • J. Hopcroft, J. Ullman
  • Computer Science
    Addison-Wesley series in computer science and information processing
  • 1969
TLDR
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
Finite-Turn Pushdown Automata
TLDR
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.
Syntax-Directed Transduction
TLDR
Some special conditions are investigated under which syntax-directed translations can be performed on (deterministic) pushdown machines and some time bounds for translations on Turing machines are derived.
On uniformity within NC 1 .
TLDR
It is shown that Immerman's families of circuits deened by rst-order formulas and Buss' deterministic log-time reductions are equivalent, leading to a natural notion of uniformity for low-level circuit complexity classes.
On Uniformity within NC¹
...
...